CK-12 Basic Geometry Teacher s Edition - Assessment

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2 To access a customizable version of this book, as well as other interactive content, visit CK-12 Foundation is a non-profit organization with a mission to reduce the cost of textbook materials for the K-12 market both in the U.S. and worldwide. Using an open-content, web-based collaborative model termed the FlexBook, CK-12 intends to pioneer the generation and distribution of high-quality educational content that will serve both as core text as well as provide an adaptive environment for learning, powered through the FlexBook Platform. Copyright 2011 CK-12 Foundation, The names CK-12 and CK12 and associated logos and the terms FlexBook, and FlexBook Platform, (collectively CK-12 Marks ) are trademarks and service marks of CK-12 Foundation and are protected by federal, state and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link (placed in a visible location) in addition to the following terms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/Non-Commercial/Share Alike 3.0 Unported (CC-by-NC-SA) License ( as amended and updated by Creative Commons from time to time (the CC License ), which is incorporated herein by this reference. Complete terms can be found at Printed: August 10, 2011

3 Editor Lori Jordan i

4 Contents 1 Basics of Geometry Assessment:Chapter Quiz 1 A: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Quiz 1 B: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Quiz 1 C: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Quiz 2 A: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Quiz 2 B: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Quiz 2 C: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Quiz 3 A: Sections 5 and 6: Angle Pairs and Classifying Polygons Quiz 3 B: Sections 5 and 6: Angle Pairs and Classifying Polygons Quiz 3 C: Sections 5 and 6: Angle Pairs and Classifying Polygons Free Response Test Multiple Choice Test Answers for Chapter 1 Assessment Reasoning and Proof Assessment:Chapter Quiz 1 A: Sections 1 and 2: Inductive Reasoning and Conditional Statements Quiz 1 B: Sections 1 and 2: Inductive Reasoning and Conditional Statements Quiz 1 C: Sections 1 and 2: Inductive Reasoning and Conditional Statements Quiz 2 A: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties Quiz 2 B: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties Quiz 2 C: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties Quiz 3 A: Section 5: Proofs about Angle Pairs and Segments Quiz 3 B: Section 5: Proofs about Angle Pairs and Segments Quiz 3 C: Section 5: Proofs about Angle Pairs and Segments Free Response Test Multiple Choice Test Answers for Chapter 2 Assessment ii

5 3 Parallel and Perpendicular Lines Assessment:Chapter Quiz 1 A: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Quiz 1 B: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Quiz 1 C: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Quiz 2 A: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines Quiz 2 B: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines Quiz 2 C: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines Quiz 3 A: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula Quiz 3 B: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula Quiz 3 C: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula Free Response Test Multiple Choice Test Answers for Chapter 3 Assessment Triangles and Congruence Assessment:Chapter Quiz 1 A: Sections 1 and 2: Triangle Sums and Congruent Figures Quiz 1 B: Sections 1 and 2: Triangle Sums and Congruent Figures Quiz 1 C: Sections 1 and 2: Triangle Sums and Congruent Figures Quiz 2 A: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Quiz 2 B: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Quiz 2 C: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Quiz 3 A: Section 5: Isosceles and Equilateral Triangles Quiz 3 B: Section 5: Isosceles and Equilateral Triangles Quiz 3 C: Section 5: Isosceles and Equilateral Triangles Free Response Test Multiple Choice Test Answers for Chapter 4 Assessment Relationships with Triangles Assessment:Chapter Quiz 1 A: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles Quiz 1 B: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles iii

6 5.3 Quiz 1 C: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles Quiz 2 A: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Quiz 2 B: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Quiz 2 C: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Quiz 3: Extension: Indirect Proof Free Response Test Multiple Choice Test Answers for Chapter 5 Assessment Polygons and Quadrilaterals Assessment:Chapter Quiz 1 A: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms Quiz 1 B: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms Quiz 1 C: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms Quiz 2 A: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares Quiz 2 B: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares Quiz 2 C: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares Quiz 3 A: Section 5: Trapezoids and Kites Quiz 3 B: Section 5: Trapezoids and Kites Quiz 3 C: Section 5: Trapezoids and Kites Free Response Test Multiple Choice Test Answers for Chapter 6 Assessment Similarity Assessment:Chapter Quiz 1 A: Sections 1 and 2: Ratios and Proportions and Similar Polygons Quiz 1 B: Sections 1 and 2: Ratios and Proportions and Similar Polygons Quiz 1 C: Sections 1 and 2: Ratios and Proportions and Similar Polygons Quiz 2 A: Sections 3 and 4: Similarity by AA, SSS and SAS Quiz 2 B: Sections 3 and 4: Similarity by AA, SSS and SAS Quiz 2 C: Sections 3 and 4: Similarity by AA, SSS and SAS Quiz 3 A: Sections 5 and 6: Proportionality Relationships and Similarity Transformations Quiz 3 B: Sections 5 and 6: Proportionality Relationships and Similarity Transformations Quiz 3 C: Sections 5 and 6: Proportionality Relationships and Similarity Transformations iv

7 7.10 Quiz 4: Extension: Self-Similarity Free Response Test Multiple Choice Test Answers for Chapter 7 Assessment Right Triangle Trigonometry Assessment:Chapter Quiz 1 A: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Quiz 1 B: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Quiz 1 C: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Quiz 2 A: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Quiz 2 B: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Quiz 2 C: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Quiz 3 A: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles Quiz 3 B: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles Quiz 3 C: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles Free Response Test Multiple Choice Test Answers for Chapter 8 Assessment Circles Assessment:Chapter Quiz 1 A: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Quiz 1 B: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Quiz 1 C: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Quiz 2 A: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 2 B: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 2 C: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 3 A: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Quiz 3 B: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Quiz 3 C: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Quiz 4: Extension: Equations of Circles Free Response Test Multiple Choice Test Answers for Chapter 9 Assessment Perimeter and Area Assessment:Chapter Quiz 1 A: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons v

8 10.2 Quiz 1 B: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons Quiz 1 C: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons Quiz 2 A: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Quiz 2 B: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Quiz 2 C: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Free Response Test Multiple Choice Test Answers for Chapter 10 Assessment Surface Area and Volume Assessment:Chapter Quiz 1 A: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Quiz 1 B: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Quiz 1 C: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Quiz 2 A: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Quiz 2 B: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Quiz 2 C: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Quiz 4: Extension: Similar Solids Free Response Test Multiple Choice Test Answers for Chapter 11 Assessment vi

9 Chapter 1 Basics of Geometry Assessment:Chapter Quiz 1 A: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Use the diagram below to answer questions 1 through Name 3 collinear points. 2. Name 4 non-coplanar points. 3. Describe the intersection of planes Q and R. 4. Name a ray. 5. Name the line which intersects plane R. 6. What is the length of the segment below? 7. What is the length of the segment below? 8. Sketch and label segment with endpoints L and K and point M between them. 1

10 9. Using your sketch from question 8, find KM if LM is 6 cm and LK is 13 cm. 10. Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. You may wish to draw a sketch to help set up your equation. HJ = x 2, JK = x + 3, KH = Quiz 1 B: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Use the diagram below to answer questions 1 through Name 3 collinear points. 2. Name 4 non-coplanar points. 3. Describe the intersection of planes Q and R. 4. Name a ray. 5. Name the line which intersects plane R. 6. What is the length of the segment below? 7. What is the length of the segment below? 8. Sketch and label segment with endpoints L and K and point M between them. 9. Using your sketch from question 8, find KM if LM is 8 cm and LK is 16 cm. 10. Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. You may wish to draw a sketch to help set up your equation. HJ = 3x 4, JK = 2x + 10, KH = Quiz 1 C: Sections 1 and 2: Points, Lines and Planes and Segments and Distance Use the diagram below to answer questions 1 through

11 1. Name 3 collinear points. 2. Name 4 non-coplanar points. 3. Describe the intersection of planes Q and R. 4. Name a ray. 5. Name the line which intersects plane R. 6. What is the length of the segment below? 7. What is the length of the segment below? 8. Sketch and label segment with endpoints L and K and point M between them. 9. Using your sketch from question 8, find KM if LM is 9 cm and LK is 19 cm. 10. Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. You may wish to draw a sketch to help set up your equation. HJ = 2x + 7, JK = 5x + 3, KH = Quiz 2 A: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Find the measure of each angle

12 2. 3. Use a protractor to make an angle with measure 48. Fill in the blanks. 4. A(n) angle has a measure between 90 and lines meet at a right angle. 6. Geometric constructions are made using a and straightedge. 7. A segment divides a segment into two congruent halves. 8. A perpendicular bisector passes through the of a segment. 9. An angle bisector divides an angle into two angles. 10. A(n) angle has a measure between 0 and 90 Find the value of x below. 11. Line m bisects AB. 12. BD bisects ABC 1.5 Quiz 2 B: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Find the measure of each angle. 4

13 Use a protractor to make an angle with measure 78. Fill in the blanks. 4. A(n) angle has a measure between 0 and An angle divides an angle into two congruent angles. 6. Geometric constructions are made using a compass and. 7. A segment bisector divides a segment into two parts. 8. A perpendicular bisector passes through the of a segment. 9. lines meet at a right angle. 10. A(n) angle has a measure between 90 and 180 Find the value of x below. 11. Line m bisects AB. 12. BD bisects ABC 5

14 1.6 Quiz 2 C: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors Find the measure of each angle Use a protractor to make an angle with measure 132. Fill in the blanks. 4. A(n) angle has a measure of A perpendicular bisector of a segment passes through the of a segment. 6. A angle bisector divides an angle into two angles. 7. Perpendicular lines meet at a angle. 8. A segment divides a segment into two congruent parts. 9. Geometric constructions are made using a and straightedge. 10. A(n) angle has a measure of between 90 and 180 Find the value of x below. 11. Line m bisects AB. 12. BD bisects ABC 6

15 1.7 Quiz 3 A: Sections 5 and 6: Angle Pairs and Classifying Polygons Fill in the blanks with sometimes, always or never. 1. Supplementary angles add up to Linear pairs are adjacent. 3. Scalene triangles have three congruent sides. 4. Diagonals in a polygon are sides of the polygon. 5. Vertical angles are complementary. 6. Adjacent angles are congruent. 7. Supplementary angles are adjacent. Find the measures of the numbered angles. 8. m 1 = 9. m 2 = 10. m 3 = Find the value of x in the diagrams below

16 Name a polygon with five sides. 14. Classify a triangle with one angle greater than 90 and two sides congruent Sketch a concave hexagon. 1.8 Quiz 3 B: Sections 5 and 6: Angle Pairs and Classifying Polygons Fill in the blanks with sometimes, always or never. 1. Complementary angles add up to Linear pairs are adjacent. 3. Equilateral triangles have three congruent sides. 4. Diagonals in a polygon are sides of the polygon. 5. Vertical angles are congruent. 6. Linear pairs are congruent. 7. Supplementary angles are adjacent. Find the measures of the numbered angles. 8. m 1 = 9. m 2 = 10. m 3 = Find the value of x in the diagrams below. 8

17 Name a polygon with six sides. 14. Classify a triangle with all angles less than 90 and two sides congruent Sketch a concave heptagon. 1.9 Quiz 3 C: Sections 5 and 6: Angle Pairs and Classifying Polygons Fill in the blanks with sometimes, always or never. 1. Complementary angles add up to Linear pairs are complementary. 3. Supplementary angles are adjacent. 4. Vertical angles are congruent. 5. Diagonals in a polygon are sides of the polygon. 6. Linear pairs are congruent. 7. Equilateral triangles have three congruent sides. Find the measures of the numbered angles. 8. m 1 = 9. m 2 = 9

18 10. m 3 = Find the value of x in the diagrams below Name a polygon with nine sides. 14. Classify a triangle with all angles less than 90 and no sides congruent Sketch a concave pentagon Free Response Test Decide whether the following statements are True or False. 1. The intersection of planes Y and Z is S V. 2. OP lies in planes Y and Z. 3. Points R, S, P and T are coplanar. 4. Points O, P, and Q are collinear. 5. Points U, S and V lie in planes Y and Z. 6. Find the length of the segment below. 10

19 7. Find the length of the segment below. For problems 8-10, points L, M and N are arranged on a line such that M is between L and N. 8. Make a sketch and label points L, M and N. 9. If LN = 23 and MN = 14, find LM. 10. If LM = 4x 2, MN = 3x + 5 and LN = 45, find x. Use a protractor to make the angles with the following degree measures Classify the following angles as acute, right, obtuse or straight Find the measure of 1 in the diagrams for questions

20 m ABC = BD is the angle bisector of ABC. Find x = m ABD = m ABC = 20. CD is a perpendicular bisector of AB. Find x = Find y = AM = AB = Fill in the blanks. 21. A polygon with 8 sides is called a(n). 22. A in a polygon connects two vertices but is not a side. 23. A triangle with all angles less than 90 degrees is called. 24. angles add up to The point halfway between two points is called the. 26. Two angles which add up to 90 are called angles. 27. A polygon with 10 sides is called a(n). 12

21 28. A(n) divides an angle into two congruent angles. 29. A point, line or ray which passes through the midpoint of a segment is called a. 30. The midpoint of a segment divides the segment into two segments Multiple Choice Test Use the diagram to the right to answer questions Which three points are collinear? (a) H, J, D (b) D, E, F (c) A, B, C (d) F, E, G 2. Which is not the intersection of planes W and V? (a) FD (b) FE (c) DE (d) GF 3. Which four points are coplanar? (a) C, B, A, F (b) H, J, D, G (c) H, J, D, C (d) D, E, B, C Use the diagram to answers questions 4 and Which segment has a length of 3 cm? (a) BC (b) CD (c) BD (d) BA 13

22 5. Which segment has a length of 4.5 cm? (a) AC (b) CD (c) BD (d) BA For questions 6-8, points P, Q, and R are collinear and Q lies between P and R. 6. PR = 37 and RQ = 12, Find PQ. (a) 49 (b) 23 (c) 25 (d) PQ = QR = 11. Find PR. (a) 11 (b) 22 (c) 33 (d) QR = 5x, PQ = 3x + 2 and PR = 9x 3. Find x. (a) 5 (b) 6 (c) 3 (d) 4 9. Find the measure of the angle. (a) 87 (b) 93 (c) 97 (d) Classify the angle in question 9. (a) right (b) acute (c) obtuse (d) straight 14

23 Use the following choices for problems (a) congruent (b) always (c) never (d) sometimes 11. Vertical angles are. 12. A perpendicular bisector passes through the midpoint of a segment. 13. Points on an angle bisector are in the exterior of the angle. 14. Linear pairs are supplementary. 15. Adjacent angles are congruent. Solve for x in the following diagrams (a) 3 (b) 4 (c) 5 (d) (a) 11 (b) 15 (c) 14 (d) (a) 5 (b) 6 (c) 7 (d)

24 (a) 10 (b) 11 (c) 4 (d) 5 Find the midpoint between the following pairs of points. 20. (5, 9) and (-1, 3) (a) (6, 2) (b) (2, 6) (c) (3, 3) (d) (7, 1) 21. (-4, 1) and (0, 7) (a) (-2, 4) (b) (4, -2) (c) (-2, 3) (d) (4, 3) Classify the following polygons (a) equilateral triangle (b) obtuse scalene triangle (c) obtuse isosceles triangle (d) acute scalene triangle (a) pentagon (b) hexagon (c) heptagon (d) quadrilateral 24. Which of the following is not a polygon. (a) (b) 16

25 (c) (d) 25. Which of the following is not a quadrilateral. (a) (b) (c) (d) 1.12 Answers for Chapter 1 Assessment Quiz 1 A: Sections 1 and 2: Points, Lines and Planes and Segments and Distance 1. E, D, C 2. Answers may vary, possible answers: E, D, B, F or F, D, G, H 3. ED, EC or DC 4. AB 5. GH 6. 5 cm cm KM = x = 18, HJ = 16, JK = 21 Quiz 1 B: Sections 1 and 2: Points, Lines and Planes and Segments and Distance 17

26 1. A, B, C 2. Answers may vary, possible answers: B, C, E, D or G, A, E, H 3. AB, BC or AC 4. EF 5. GH cm 7. 5 cm KM = x = 7, HJ = 17, JK = 24 Quiz 1 C: Sections 1 and 2: Points, Lines and Planes and Segments and Distance 1. M, N, O 2. Answers may vary, possible answers: N, O, S, P or T, S, P, L 3. MN, NO or MO 4. S T 5. LK 6. 5 cm cm KM = x = 6, HJ = 19, JK = 33 Quiz 2 A: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors obtuse 5. perpendicular 6. compass 7. bisector 8. midpoint 9. congruent 10. acute 11. x = x = 5 Quiz 2 B: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors

27 acute 5. bisector 6. straightedge 7. congruent 8. midpoint 9. perpendicular 10. obtuse 11. x = x = 14 Quiz 2 C: Sections 3 and 4: Angles and Measurement, Midpoints and Bisectors straight 5. midpoint 6. congruent 7. right 8. bisector 9. compass 10. obtuse 11. x = x = 11 Quiz 3 A: Sections 5 and 6: Angle Pairs and Classifying Polygons 1. always 2. always 3. never 4. never 5. sometimes 6. sometimes 7. sometimes

28 pentagon 14. obtuse isosceles 15. answers will vary, possible sketch: Quiz 3 B: Sections 5 and 6: Angle Pairs and Classifying Polygons 1. never 2. always 3. always 4. never 5. always 6. sometimes 7. sometimes hexagon 14. acute isosceles 15. answers will vary, possible sketch: Quiz 3 C: Sections 5 and 6: Angle Pairs and Classifying Polygons 1. always 2. never 3. sometimes 4. always 5. never 6. sometimes 7. always nonagon 20

29 14. acute scalene 15. answers will vary, possible sketch: Free Response Test 1. True 2. False 3. False 4. True 5. True cm 7. 7 cm LM = x = acute 14. right 15. straight x = 27, m ABD = 60, m ABC = x = 5, y = 16, AM = 18, AB = octagon 22. diagonal 23. acute 24. supplementary 25. midpoint 26. complementary 27. decagon 28. angle bisector 29. segment bisector 21

30 30. congruent Multiple Choice Test 1. b 2. d 3. c 4. d 5. a 6. c 7. b 8. a 9. b 10. c 11. a 12. b 13. c 14. b 15. d 16. b 17. d 18. b 19. d 20. b 21. a 22. b 23. a 24. c 25. d 22

31 Chapter 2 Reasoning and Proof Assessment:Chapter Quiz 1 A: Sections 1 and 2: Inductive Reasoning and Conditional Statements 1. Draw the next figure in the pattern. Describe the pattern and write the next two terms in the sequence. 2. 3, 5, 7,, 3. 81, 27, 9,, 4. Fill in the blanks to complete the sequence: 1, 4, 9,, 25,, 49 Give a counterexample for each of the following statements. 5. All quadrilaterals are convex. 6. Congruent angles are always adjacent. In the following conditional statements, circle the hypothesis and underline the conclusion. 7. If it rains, then I will use my umbrella. 8. I do well on quizzes when I do my homework. For questions 9-11 use the statement: If I go to the mall, then I will buy a pair of shoes. 9. Write the converse of the statement. 23

32 10. Write the inverse of the statement. 11. Write the contrapositive of the statement. 12. Which statement is logically equivalent to the original statement? 13. Split the following biconditional statement into a statement and its converse. Three points are collinear if and only if they lie on the same line. 14. Write the converse of the statement: If an angle measures 90, it is a right angle. 15. Is the statement you wrote for #13 true? If so, write a biconditional statement. 2.2 Quiz 1 B: Sections 1 and 2: Inductive Reasoning and Conditional Statements 1. Draw the next figure in the pattern. Describe the pattern and write the next two terms in the sequence , 10, 7,, 3. 2, 4, 8,, 4. Fill in the blanks to complete the sequence: 1, 4, 9,, 25,, 49 Give a counterexample for each of the following statements. 5. All numbers that end in 4 are divisible by All pentagons are convex. In the following conditional statements, circle the hypothesis and underline the conclusion. 7. If it snows, then I will make a snowman. 8. I feel energized when I go for a run. For questions 9-11 use the statement: If I go to the mall, then I will buy a new hat. 9. Write the inverse of the statement. 10. Write the converse of the statement. 11. Write the contrapositive of the statement. 12. Which statement is logically equivalent to the original statement? 13. Split the following biconditional statement into a statement and its converse. Two angles are congruent if and only if they have the same measure. 14. Write the converse of the statement: If a polygon has six sides, then it is a hexagon. 15. Is the statement you wrote for #13 true? If so, write a biconditional statement. 24

33 2.3 Quiz 1 C: Sections 1 and 2: Inductive Reasoning and Conditional Statements 1. Draw the next figure in the pattern. Describe the pattern and write the next two terms in the sequence. 2. 9, 13, 17,, 3. 48, 24, 12,, 4. Fill in the blanks to complete the sequence: 1, 4, 9,, 25,, 49 Give a counterexample for each of the following statements. 5. All numbers greater than 9 that end in 9 are prime numbers. 6. All quadrilaterals are convex. In the following conditional statements, circle the hypothesis and underline the conclusion. 7. I always wear sunscreen when I go to the beach. 8. If I study, then I get good grades. For questions 9-11 use the statement: If I go for a drive, then I will listen to music. 9. Write the inverse of the statement. 10. Write the contrapositive of the statement. 11. Write the converse of the statement. 12. Which statement is logically equivalent to the original statement? 13. Split the following biconditional statement into a statement and its converse. Two adjacent angles form a linear pair if and only if their nonadjacent sides form a line. 14. Write the converse of the statement: If a polygon has eight sides, then it is a octagon. 15. Is the statement you wrote for #13 true? If so, write a biconditional statement. 2.4 Quiz 2 A: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. Identify the following as examples of inductive or deductive reasoning. 1. Students performing a lab in science class and making a conjecture. 25

34 2. A crime scene investigator checking the fingerprints found at a crime scene against known criminals for a match. 3. Finding the next term in a sequence. 4. Using a formula to find the area of a figure. Decide whether the following arguments are example of Law of Detachment, Law of Syllogism, Law of the Contrapositive or Invalid. 5. If I go for a walk, then I take my dog. I take my dog. Therefore, I go for a walk. 6. If it is Friday, then we order pizza. Therefore, if we don t order pizza, then it isn t Friday. 7. If we make eggs, we make green eggs. If we make green eggs, then we must have ham. Therefore, if we make eggs, then we must have ham. 8. If you like cookies, then you like milk. You like cookies. Therefore, you like milk. Determine which properties of algebra or congruence are used to make the conclusion. 9. If x + 8 = 23, then x = If x = 9 and 9 = y, then x = y. 11. If 7x = 42, then x = If x = y, then y = x. 13. If x = 11, then x + 9 = C C 15. 2(x + 3) = 2x Quiz 2 B: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. Identify the following as examples of inductive or deductive reasoning. 1. Solving an equation for x. 2. Students performing a lab in science class and making a conjecture. 3. Using a formula to find the area of a figure. 4. Finding the next term in a sequence. Decide whether the following arguments are example of Law of Detachment, Law of Syllogism, Law of the Contrapositive or Invalid. 5. If we make eggs, we make green eggs. If we make green eggs, then we must have ham. Therefore, if we make eggs, then we must have ham. 6. If I eat spicy food for dinner, then I have crazy dreams. Therefore, if I don t have crazy dreams, then I didn t eat spicy food for dinner. 7. If I go for a walk, then I take my dog. I go for a walk. Therefore, I take my dog. 8. If you like cookies, then you like milk. You like milk. Therefore, you like cookies. Determine which properties of algebra or congruence are used to make the conclusion. 26

35 9. If 7x = 42, then x = If x = 9 and 9 = y, then x = y. 11. If x + 8 = 23, then x = (x + 3) = 2x C C 14. If x = y, then y = x. 15. If x = 11, then x + 9 = Quiz 2 C: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. Identify the following as examples of inductive or deductive reasoning. 1. Students performing a lab in science class and making a conjecture. 2. Observing data, noticing a pattern and making a conjecture. 3. A crime scene investigator checking the fingerprints found at a crime scene against known criminals for a match. 4. Solving for unknown variables in an equation. Decide whether the following arguments are example of Law of Detachment, Law of Syllogism, Law of the Contrapositive or Invalid. 5. If we go to the store, then we use a shopping cart. We go to the store. Therefore, we use a shopping cart. 6. If I go for a walk, then I take my dog. I take my dog. Therefore, I go for a walk. 7. If we make eggs, we make green eggs. If we make green eggs, then we must have ham. Therefore, if we make eggs, then we must have ham. 8. If you like cookies, then you like milk. Therefore, If you don t like milk, then you don t like cookies. Determine which properties of algebra or congruence are used to make the conclusion. 9. If x = 11, then x + 9 = If x = y and y = z, then x = z. 11. If x + 8 = 23, then x = A A 13. If 7x = 42, then x = (x + 3) = 2x If x = y, then y = x. 2.7 Quiz 3 A: Section 5: Proofs about Angle Pairs and Segments Fill in the blanks to complete the proof. 27

36 Given: 4 is a right angle Prove: 6 and 2 are complementary Statement Table 2.1: Reason Definition of a right angle 3. m 2 + m 3 + m 4 = m 2 + m = m 2 + m 3 = m 3 = m Substitution Definition of complementary angles. Find the measures of the indicated angles in the diagram given T P VR. 10. m T OU 11. m ROQ 12. m QOV 13. m ROT 14. m UOP 15. m ROU 2.8 Quiz 3 B: Section 5: Proofs about Angle Pairs and Segments Fill in the blanks to complete the proof. 28

37 Given: 2 and 3 are complementary Prove: 1 is a right angle Statement Table 2.2: Reason Definition of complementary angles 3. m 2 + m 3 + m 4 = m 4 = m 4 = Vertical Angles Theorem 7. m 1 = Definition of a right angle Find the measures of the indicated angles in the diagram given T P VR. 10. m T OU 11. m ROQ 12. m QOV 13. m ROT 14. m UOP 15. m ROU 2.9 Quiz 3 C: Section 5: Proofs about Angle Pairs and Segments Fill in the blanks to complete the proof. 29

38 Given: 1 is a right angle Prove: 5 and 3 are complementary Statement Table 2.3: Reason definition of a right angle 3. m 1 + m 6 + m 5 = m 6 + m 5 = m 6 + m 5 = m 3 = m Substitution definition of complementary angles Find the measures of the indicated angles in the diagram given T P VR. 10. m T OU 11. m ROQ 12. m QOV 13. m ROT 14. m UOP 15. m ROU 30

39 2.10 Free Response Test 1. Draw the next figure in the pattern. Describe the pattern and write the next two terms in the sequence , 34, 27,, 3. 1, 4, 16,, Fill in the blanks in the following sequences. 4. A, C,, G,, K , 9 4,, 7 6,, 5 8 Give a counterexample to for the following conjectures. 6. Supplementary angles are always congruent. 7. All numbers greater than 3 that end in 3 are prime numbers. For questions 8-11, use the following statements. p: it snows q: I will go skiing 8. Write the conditional statement: p q. 9. Write the statement: p q. What is this statement called? 10. Write the statement: q p. What is this statement called? 11. Write the statement: q p. What is this statement called? For questions 12-14, use the statement: All vertical angles are congruent. 12. Write the statement as an if-then statement. 13. Write the converse of this statement. 14. Is the converse true? If yes, write a biconditional statement. If no, give a counterexample. Determine the logical conclusion and state which law you used (Law of Detachment, Law of Contrapositive, or Law of Syllogism). If no conclusion can be drawn, write no conclusion. 15. If it is hot outside, you wear shorts. If you wear shorts, then you wear sandals. If you wear sandals, then your feet get sunburned. If your feet get sunburned then you can t walk on them. 16. If the mailman comes to the door, the dog barks. The dog is barking. 17. If the back yard is muddy, then we make mud pies. The back yard is muddy. 18. If a figure is a square, then it is a rectangle. The figure is not a rectangle. 19. Fill in the blanks with the appropriate algebraic steps properties of equality. 31

40 Statement Table 2.4: Reason 1. 3(2x 5) = 4x Given Distributive Property 3. 2x 15 = x = Fill in the blanks in the proof below. Given: AC = BD Prove: AB = CD Statement Table 2.5: Reason AB + BC = AC and BC + CD = BD Substitution Reflexive Property of Equality Fill in the blanks in the proof below. Given: m LKM = m NKO Prove: m LKN = m MKO Statement Table 2.6: Reason m MKN = m MKN m LKM + m MKN = m MKN + m NKO Angle Addition Postulate

41 2.11 Multiple Choice Test 1. Which is the next figure in the sequence below? (a) (b) (c) (d) Fill in the blanks with the missing terms in the following sequences. 2. S, M,, W, T, (a) M; O (b) T; F (c) F; T (d) O; M ,, 2,, 9 (a) 6; 2 3 (b) 2 3 ; 6 (c) 9; 4 3 (d) 4 3 ;

42 For questions 4 and 5, Identify the counterexample for the conjecture. 4. If a > b, then a 2 > b 2. (a) a = 2, b = 1 (b) a = 1 2, b = 1 3 (c) a = 0.9, b = 0.8 (d) a = 1, b = 2 5. Given a b, if a is even and b is 9, then result is a repeating decimal. (a) a = 4 (b) a = 8 (c) a = 18 (d) a = Identify the converse of the statement: If the moon is full, then the dogs will howl. (a) If the moon is not full, then the dogs will not howl. (b) If the dogs howl, then the moon is full. (c) If the dogs do not howl, then the moon is not full. (d) If the dogs howl, then the moon is not full. 7. Identify the inverse of the statement: I swim in the ocean when I go to the beach. (a) If don t swim, then I m not at the beach. (b) If I m at the beach, then I swim. (c) If I m not at the beach, then I don t swim. (d) If I am swimming, then I am at the beach. 8. Identify the contrapositive of the statement If today is Tuesday, then tomorrow is Wednesday. (a) If tomorrow is Wednesday, then today is Tuesday. (b) If tomorrow is not Wednesday, then today is Tuesday. (c) If today is not Tuesday, then tomorrow is not Wednesday. (d) If tomorrow is not Wednesday, then today is not Tuesday. 9. Which biconditional statement is not true? (a) A triangle is scalene if and only if it has three unequal sides. (b) An angle is acute if and only if it measures between 0 and 90. (c) Angles are vertical angles if and only if they are congruent. (d) Angles are supplementary if and only if their sum is Which type of reasoning is used below: If we go for a walk in the fall, then we collect leaves. We go for a walk in the fall. Therefore, we collect leaves. (a) Law of Syllogism (b) Law of Contrapositive (c) Not Valid. (d) Law of Detachment. 11. Which type of reasoning is used below: If Tommy scores a goal, then the crowd will cheer. Therefore, if Tommy scores a goal, the baby will cry If the crowd cheers, then the baby will cry.

43 (a) Law of Syllogism (b) Law of Contrapositive (c) Not Valid. (d) Law of Detachment. 12. Which type of reasoning is used below: If it rains while the sun is shining we will see a rainbow. We did not see a rainbow. Therefore, it did not rain while the sun was shining. (a) Law of Syllogism (b) Law of Contrapositive (c) Not Valid. (d) Law of Detachment. For questions 13-16, match the properties with the examples. (a) Substitution (b) Transitive (c) Reflexive (d) Symmetric 13. If AB = BC and BC = CD, then AB = CD. 14. If B C, then C B. 15. If m 1 + m 2 = 56 and m 1 = 26, then 26 + m 2 = LM LM. Use the figure below to fill in the blanks in the proof for questions Given: m 1 = m 4 and m 2 = m 3 Prove: QS PR (a) Transitive Property of Equality (b) Definition of a Right Angle (c) Angle Addition Postulate (d) Addition Property of Equality Statement Table 2.7: Reason m 1 = m 4 and m 2 = m 3 Given m 1 + m 2 = m 4 + m m 1 + m 2 + m 3 + m 4 = 180 They form a line (Linear Pair) m 1 + m 2 + m 1 + m 2 = 180 Substitution 2(m 1 + m 2) = 180 Distributive Property 35

44 Statement Table 2.7: (continued) Reason m 1 + m 2 = 90 Division Property of Equality m 1 + m 2 = m PQS 18. m PQS = PQS is a right angle 20. QS PR Perpendicular lines form right angles 2.12 Answers for Chapter 2 Assessment Quiz 1 A: Sections 1 and 2: Inductive Reasoning and Conditional Statements add 2; 9, divide by 3; 3, ; If I bought a pair of shoes, then I went to the mall. 10. If I do not go to the mall, then I will not buy a pair of shoes. 11. If I did not buy a pair of shoes, then I did not go to the mall. 12. the contrapositive, number If three points are collinear, then they lie on the same line. If three points lie on the same line, then they are collinear. 14. If an angle is a right angle, then it measures Yes. An angle is a right angle if and only if it measures 90. Quiz 1 B: Sections 1 and 2: Inductive Reasoning and Conditional Statements 36

45 1. 2. subtract 3; 4, 1 3. multiply by 2; 16, ; Possible answer: If I do not go to the mall, then I will not buy a new hat. 10. If I bought a new hat, then I went to the mall. 11. If I did not buy a new hat, then I did not go to the mall. 12. The contrapositive, # If two angles are congruent, then they have the same measure. If two angles have the same measure, then they are congruent. 14. If a polygon is a hexagon, then it has six sides. 15. A polygon is a hexagon if and only if it has six sides. Quiz 1 C: Sections 1 and 2: Inductive Reasoning and Conditional Statements add 4; 21, divide by 2; 6, ; Possible answer:

46 9. If I do not go for a drive, then I will not listen to music. 10. If I am not listening to music, then I am not going for a drive. 11. If I am listening to music, then I am going for a drive. 12. The contrapositive, # If two adjacent angles form a linear pair, then their nonadjacent sides form a line. If the nonadjacent sides of a pair of adjacent angles form a line, then the angles form a linear pair. 14. If a polygon is an octagon, then it has eight sides. 15. Yes. A polygon is an octagon if and only if it has eight sides. Quiz 2 A: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. 1. Inductive 2. Deductive 3. Inductive 4. Deductive 5. Invalid 6. Law of Contrapositive 7. Law of Syllogism 8. Law of Detachment 9. Subtraction Property of Equality 10. Transitive Property of Equality 11. Division Property of Equality 12. Symmetric Property of Equality 13. Substitution Property of Equality 14. Reflexive Property of Congruence 15. Distributive Property Quiz 2 B: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. 1. Deductive 2. Inductive 3. Deductive 4. Inductive 5. Law of Syllogism 6. Law of Contrapositive 7. Law of Detachment 8. Invalid 9. Division Property of Equality 10. Transitive Property of Equality 11. Subtraction Property of Equality 12. Distributive Property of Equality 13. Reflexive Property of Congruence 14. Symmetric property of Equality 15. Substitution Property of Equality Quiz 2 C: Sections 3 and 4: Deductive Reasoning and Algebraic and Congruence Properties. 1. Inductive 2. Inductive 38

47 3. Deductive 4. Deductive 5. Law of Detachment 6. Invalid 7. Law of Syllogism 8. Law of the Contrapositive 9. Substitution Property of Equality 10. Transitive Property of Equality 11. Subtraction Property of Equality 12. Reflexive Property of Congruence 13. Division Property of Equality 14. Distributive Property 15. Symmetric Property of Equality Quiz 3 A: Section 5: Proofs about Angle Pairs and Segments Statement Table 2.8: Reason 1. 4 is a right angle 1. Given 2. m 4 = Definition of a right angle 3. m 2 + m 3 + m 4 = They form a line (Linear Pair) 4. m 2 + m = Substitution 5. m 2 + m 3 = Subtraction 6. m 3 = m 6 6. Vertical Angles Theorem 7. m 2 + m 6 = Substitution 8. 2 and 6 are complementary 8. Definition of complementary angles Quiz 3 A: Section 5: Proofs about Angle Pairs and Segments Statement Table 2.9: Reason 1. 2 and 3 are complementary 1. Given 2. m 2 + m 3 = Definition of complementary angles 3. m 2 + m 3 + m 4 = They form a line (Linear Pair) m 4 = Substitution 5. m 4 = Subtraction 6. m 1 = m 4 6. Vertical Angles Theorem 7. m 1 = Transitive Property of Equality 8. 1 is a right angle 8. Definition of a right angle 39

48 Quiz 3 A: Section 5: Proofs about Angle Pairs and Segments Statement Table 2.10: Reason 1. 1 is a right angle 1. Given 2. m 1 = Definition of a right angle 3. m 1 + m 6 + m 5 = They form a line (Linear Pair) m 6 + m 5 = Substitution 5. m 2 + m 3 = Subtraction 6. m 3 = m 6 6. Vertical Angles Theorem 7. m 3 + m 5 = Substitution 8. 3 and 5 are complementary 8. Definition of complementary angles Free Response Test subtract 7; 20, Multiply by 4; E; I ; any two angles which add to 180 but are not equal, such as: 27, answers vary. possible answers include: 33, 63, If it snows, then I will go skiing. 9. If it does not snow, then I will not go skiing. Inverse 10. If I do not go skiing, then it did not snow. Contrapositve 11. If I go skiing, then it snowed. Converse 12. If angles are vertical angles, then they are congruent. 13. If angles are congruent, then they are vertical angles. 40

49 14. No, the converse is false. An counter example is any pair of congruent angles which are not vertical angles. Possible drawing: 15. Therefore, if it is hot outside, then you can t walk on your feet. Law of Syllogism 16. No conclusion. 17. Therefore, we make mud pies. Law of Detachment 18. Therefore, it is not a square. Law of the Contrapositive 19. Statement Table 2.11: Reason 1. 3(2x 5) = 4x Given 2. 6x 15 = 4x Distributive Property 3. 2x 15 = 5 3. Subtraction Property of Equality 4. 2x = Addition Property of Equality 5. x = Division Property of Equality 20. Statement Table 2.12: Reason 1. AC = BD 1. Given 2. AB + BC = AC and BC + CD = BD 2. Segment Addition Postulate 3. AB + BC = BC + CD 3. Substitution 4. BC = BC 4. Reflexive Property of Equality 5. AB = CD 5. Subtraction Property of Equality 21. Statement Table 2.13: Reason 1. m LKM = m NKO 1. Given 2. m MKN = m MKN 2. Reflexive Property of Equality 3. m LKM + m MKN = m MKN + m NKO 3. Addition Property of Equality 4. m LKM + m MKN = m LKN 4. Angle Addition Postulate m MKN + m NKO = m MKO 41

50 Table 2.13: (continued) Statement Reason 5. m LKN = m MKO 5. Substitution Property of Equality Multiple Choice Test 1. a 2. b 3. a 4. d 5. c 6. b 7. c 8. d 9. c 10. d 11. a 12. b 13. b 14. d 15. a 16. c 17. d 18. c 19. a 20. b 42

51 Chapter 3 Parallel and Perpendicular Lines Assessment:Chapter Quiz 1 A: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Use the diagram of a cube to answer the questions Name a segment parallel to CD. 2. Name a segment perpendicular to AE. 3. Name a segment skew to BF. 4. Name a plane parallel to plane AEG. 5. Use a compass and straightedge to construct the perpendicular line through the given point. Use the diagram below to answer questions

52 6. Name a pair of corresponding angles. 7. Name a pair of alternate interior angles. 8. Name a pair of alternate exterior angles. 9. Name a pair of same side interior angles. Find the measures of the numbered angles given that l m. 10. m m m m m m m Quiz 1 B: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Use the diagram of a cube to answer the questions Name a plane parallel to plane AEG 2. Name a segment perpendicular to AE. 44

53 3. Name a segment parallel to CD. 4. Name a segment skew to BF. 5. Use a compass and straightedge to construct the perpendicular line through the given point. Use the diagram below to answer questions Name a pair of alternate interior angles. 7. Name a pair of same side interior angles 8. Name a pair of corresponding angles 9. Name a pair of alternate exterior angles. Find the measures of the numbered angles given that l m. 10. m m m m m m m Quiz 1 C: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines Use the diagram of a cube to answer the questions

54 1. Name a segment skew to BF. 2. Name a plane parallel to plane AEG 3. Name a segment parallel to CD. 4. Name a segment perpendicular to AE. 5. Use a compass and straightedge to construct the perpendicular line through the given point. Use the diagram below to answer questions Name a pair of same side interior angles. 7. Name a pair of corresponding angles. 8. Name a pair of alternate exterior angles. 9. Name a pair of alternate interior angles. Find the measures of the numbered angles given that l m. 10. m m m m

55 14. m m m Quiz 2 A: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines In questions 1-3, find the measure of 1, which makes a b In questions 4 and 5, find the measure of 1, which makes a b

56 Find the value of x in the following diagrams Given: 2 and 4 are supplementary Prove: m n Statement Table 3.1: Reason Definition of supplementary m 2 + m 1 = m 2 + m 1 = m 2 + m 4 Transitive m 2 = m m 1 = m 4 Subtraction Property of Equality

57 3.5 Quiz 2 B: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines In questions 1-3, find the measure of 1, which makes a b In questions 4 and 5, find the measure of 1, which makes a b Find the value of x in the following diagrams. 49

58 Given: 2 and 4 are supplementary Prove: m n Statement Table 3.2: Reason Definition of supplementary m 2 + m 1 = m 2 + m 1 = m 2 + m 4 Transitive m 2 = m m 1 = m 4 Subtraction Property of Equality Quiz 2 C: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines In questions 1-3, find the measure of 1, which makes a b. 50

59 In questions 4 and 5, find the measure of 1, which makes a b Find the value of x in the following diagrams

60 7. 8. Given: 2 and 4 are supplementary Prove: m n Statement Table 3.3: Reason Definition of supplementary m 2 + m 1 = m 2 + m 1 = m 2 + m 4 Transitive m 2 = m m 1 = m 4 Subtraction Property of Equality Quiz 3 A: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula Decide whether AB and CD are parallel, perpendicular or neither. 1. A(4, 9), B(5, 3) C(5, 2), D( 1, 3) 2. A( 4, 8), B(1, 2) 52

61 C( 7, 15), D( 6, 13) 3. A(0, 2), B( 5, 3) C(3, 8), D( 2, 6) Write the equation of the line through the given slope and point. 4. m = 2 5 ; (10, 7) 5. m = 3; ( 1, 2) 6. m = 3 7 ; (21, 2) 7. Write the equation of the line parallel to y = 2x 5 through (-1, 3). 8. Write the equation of the line perpendicular to y = 5 3 x + 3 through (10, -7). Find the distance between the following pairs of points. 9. (5, -2) and (-1, -10) 10. (-4, 11) and (4, 26) 3.8 Quiz 3 B: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula 1. A(4, 9), B(5, 3) C( 1, 2), D(0, 7) 2. A( 4, 8), B(1, 2) C( 8, 3), D( 6, 4) 3. A(0, 2), B( 5, 3) C(1, 7), D(11, 5) Write the equation of the line through the given slope and point. 4. m = 2 3 ; (6, 7) 5. m = 5; ( 9, 2) 6. m = 4 7 ; (14, 2) 7. Write the equation of the line parallel to y = 2x 5 through (-1, 3). 8. Write the equation of the line perpendicular to y = 5 3 x + 3 through (10, -7). Find the distance between the following pairs of points. 9. (5, -2) and (2, -6) 10. (-4, 11) and (3, 35) 3.9 Quiz 3 C: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula 1. A(4, 9), B(5, 3) C(3, 5), D(2, 1) 53

62 2. A( 4, 8), B(1, 2) C(8, 3), D(6, 4) 3. A(0, 2), B( 5, 3) C( 1, 2), D(0, 7) Write the equation of the line through the given slope and point. 4. m = 2 3 ; (6, 7) 5. m = 5; ( 9, 4) 6. m = 5 7 ; (14, 2) 7. Write the equation of the line parallel to y = 3x 5 through (-1, 3). 8. Write the equation of the line perpendicular to y = 3 5 x + 3 through (-6, 7). Find the distance between the following pairs of points. 9. (5, -3) and (1, -6) 10. (-4, 11) and (11, 19) 3.10 Free Response Test Use the diagram to answer questions Name a segment skew to S R. 2. Name a plane parallel to plane NRQ. 3. Name a line parallel to LP. 4. Name a line perpendicular to MN. Find the value of x in the diagrams below

63 Decide whether the lines are parallel, perpendicular or neither. 11. y = 3x + 11 and y = 3x y = 1 4 x 7 and y = 4x Write the equation of the line parallel to y = 2 5 x 9 through (-10, 2) 14. Write the equation of the line perpendicular to y = x + 3 through (8, -4) Fill in the blanks for the proof below. Given: 1 3 Prove: 1 and 4 are supplementary 55

64 Statement Table 3.4: Reason m n 17. m 3 + m 4 = Substitution 1 and 4 are supplementary 20. Given: m n Prove: 2 and 3 are supplementary Statement Table 3.5: Reason m 2 = m Linear Pair m 3 + m 2 = and 3 are supplementary Find the distance between the points (3, -7) and (-2, 5). 28. What is the distance between the lines with equations x = 2 and x = 5? 3.11 Multiple Choice Test Use the diagram and the choices below to answer questions 1-5. (a) Skew 56

65 (b) Perpendicular (c) Parallel (d) None of these 1. DC and CH are. 2. HG and CB are. 3. AB and BC are. 4. Plane EDC and Plane HGF are. 5. DC and FG are. For questions 6-10, decide what the relationship between the pairs of angles is. (a) Congruent (b) Supplementary (c) Complementary (d) None of these 6. 1 and 7 are and 4 are and 9 are and 7 are and 5 are. For questions 11-17, find the value of x in each diagram. 57

66 (a) 72 (b) 108 (c) 18 (d) (a) 112 (b) 102 (c) 68 (d) (a) 52 (b) 36 (c) 62 (d) 46 (a) 65 (b) 30 (c) 75 (d)

67 15. (a) 33 (b) 20 (c) 23 (d) (a) 20 (b) 26 (c) 22 (d) Write the equation of the line parallel to y = 3 4 x + 5 through (8, -4). (a) y = 3 4 x + 5 (b) y = 3 4 x 10 (c) y = 4 3 x + 10 (d) y = 3 4 x Write the equation of the line perpendicular to y = 5x + 1 through (-10, 3). (a) y = 5x + 53 (b) y = 5x 47 (c) y = 1 5 x + 5 (d) y = 1 5 x Find the distance between the points (9, -1) and (6, 3). (a) 25 (b) 5 (c) 1 (d) 7 Fill in the blanks to complete the proof below. 59

68 Given: m n Prove: m 1 + m 2 + m 3 = 180 (a) Alternate Interior Angles Theorem (b) Substitution (c) Corresponding Angles Theorem (d) Reflexive Property Statement Table 3.6: Reason m n Given m 5 = m 3 and m 4 = m m 5 + m 2 + m 4 = 180 Linear Pair m 1 + m 2 + m 3 = Answers for Chapter 3 Assessment Quiz 1 A: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines 1. GH, AB or EF 2. EF, AB, AC or EG 3. GH, CD, AC or EG 4. plane BFH and 5, 2 and 6, 3 and 7 or 4 and and 6 or 3 and and 7 or 2 and and 5 or 3 and

69 Quiz 1 B: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines 1. plane BFH 2. EF, AB, AC or EG 3. GH, AB or EF 4. GH, CD, AC or EG and 6 or 3 and and 5 or 3 and and 5, 2 and 6, 3 and 7 or 4 and and 7 or 2 and Quiz 1 C: Sections 1 and 2: Lines and Angles and Properties of Parallel Lines 1. GH, CD, AC or EG 2. plane BFH 3. GH, AB or EF 4. EF, AB, AC or EG and 5 or 3 and and 5, 2 and 6, 3 and 7 or 4 and and 7 or 2 and and 6 or 3 and

70 Quiz 2 A: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines x = x = 9 8. x = 9 Statement Table 3.7: Reason 9. 2 and 4 are supplementary 10. Given 11. m 2 + m 4 = 180 Definition of supplementary m 2 + m 1 = Linear Pair m 2 + m 1 = m 2 + m 4 Transitive m 2 = m Reflexive m 1 = m 4 Subtraction Property of Equality 14. m n 15. Converse of Corrsponding Angles Theorem Quiz 2 B: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines x = x = x = 15 Statement Table 3.8: Reason 9. 2 and 4 are supplementary 10. Given 11. m 2 + m 4 = 180 Definition of supplementary m 2 + m 1 = Linear Pair m 2 + m 1 = m 2 + m 4 Transitive m 2 = m Reflexive m 1 = m 4 Subtraction Property of Equality 14. m n 15. Converse of Corrsponding Angles Theorem 62

71 Quiz 2 C: Sections 3 and 4: Proving Lines Parallel and Properties of Perpendicular Lines x = 9 7. x = x = 8 Statement Table 3.9: Reason 9. 2 and 4 are supplementary 10. Given 11. m 2 + m 4 = 180 Definition of supplementary m 2 + m 1 = Linear Pair m 2 + m 1 = m 2 + m 4 Transitive m 2 = m Reflexive m 1 = m 4 Subtraction Property of Equality 14. m n 15. Converse of Corrsponding Angles Theorem Quiz 3 A: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula 1. perpendicular 2. parallel 3. neither 4. y = 2 5 x y = 3x 1 6. y = 3 7 x y = 2x y = 3 5 x Quiz 3 B: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula 1. neither 2. perpendicular 3. parallel 4. y = 2 3 x y = 5x y = 4 7 x y = 2x y = 3 5 x

72 Quiz 3 C: Sections 5 and 6: Parallel and Perpendicular Lines in the Coordinate Plane and the Distance Formula 1. parallel 2. neither 3. perpendicular 4. y = 2 3 x y = 5x y = 5 7 x y = 3x 8. y = 5 3 x Free Response Test 1. NM, OL, QM or PL 2. OS P 3. MQ, NR or OS 4. NO, NR, MQ or ML Neither 12. Perpendicular 13. y = 2 5 x y = x Given 17. Converse of the Alternate Interior Angles Theorem 18. Linear Pair 19. m 3 + m 4 = Definition of Supplementary 21. m n 22. Given 23. Corresponding Angles Theorem 24. m 3 + m 2 = Substitution 26. Definition of Supplementary Multiple Choice Test 1. b 64

73 2. c 3. d 4. c 5. a 6. a 7. b 8. c 9. d 10. a 11. b 12. c 13. d 14. a 15. c 16. d 17. b 18. d 19. b 20. a 21. b 65

74 Chapter 4 Triangles and Congruence Assessment:Chapter Quiz 1 A: Sections 1 and 2: Triangle Sums and Congruent Figures Find the value of x in questions

75 5. 6. For questions 7-11, use the congruence statement: XYZ WVU 7. Y 8. XZ 9. If m Z = 87, then m U = 10. If YZ = 8, then UV = 11. If m X = 73 and m Y = 51, then m U = 4.2 Quiz 1 B: Sections 1 and 2: Triangle Sums and Congruent Figures Find the value of x in questions

76 5. 6. For questions 7-11, use the congruence statement: XYZ WVU 7. Z 8. XY 9. If m Z = 84, then m U = 10. If YZ = 9, then UV = 11. If m X = 63 and m Y = 72, then m U = 4.3 Quiz 1 C: Sections 1 and 2: Triangle Sums and Congruent Figures Find the value of x in questions

77 5. 6. For questions 7-11, use the congruence statement: XYZ WVU 7. X 8. YZ 9. If m Z = 89, then m U = 10. If YZ = 11, then UV = 11. If m X = 59 and m Y = 77, then m U = 4.4 Quiz 2 A: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Use the figure to answer questions Name the side included between A and B. 2. Name the angle included between sides AB and BC. 3. Name a side not included between A and C. For the pairs of triangles below, give the triangle congruence statement and the theorem used to prove they are congruent

78 The triangles in questions 8 and 9 are not congruent. Explain why they are not congruent Quiz 2 B: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Use the figure to answer questions

79 1. Name the side included between C and B. 2. Name the angle included between sides AC and BC. 3. Name a side not included between A and B. For the pairs of triangles below, give the triangle congruence statement and the theorem used to prove they are congruent The triangles in questions 8 and 9 are not congruent. Explain why they are not congruent. 71

80 Quiz 2 C: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL Use the figure to answer questions Name the side included between C and A. 2. Name the angle included between sides AC and BA. 3. Name a side not included between C and B. For the pairs of triangles below, give the triangle congruence statement and the theorem used to prove they are congruent

81 The triangles in questions 8 and 9 are not congruent. Explain why they are not congruent Quiz 3 A: Section 5: Isosceles and Equilateral Triangles Fill in the blanks below using the diagram. RAC is isosceles with vertex angle bisector AE 73

82 1. RA 2. R 3. RAE 4. ER 5. AE Solve for x in the problems below Find the measures of the indicated angles in the diagram below. 8. w = 9. x = 74

83 10. y = 11. z = 4.8 Quiz 3 B: Section 5: Isosceles and Equilateral Triangles Fill in the blanks below using the diagram. RAC is isosceles with vertex angle bisector AE 1. ER 2. AE 3. RAE 4. RA 5. R Solve for x in the problems below Find the measures of the indicated angles in the diagram below. 75

84 8. w = 9. x = 10. y = 11. z = 4.9 Quiz 3 C: Section 5: Isosceles and Equilateral Triangles Fill in the blanks below using the diagram. RAC is isosceles with vertex angle bisector AE 1. ER 2. AE 3. RAE 4. R 5. RA Solve for x in the problems below

85 7. Find the measures of the indicated angles in the diagram below. 8. w = 9. x = 10. y = 11. z = 4.10 Free Response Test Find the value of x in questions

86 In questions 11-14, state the congruent parts required to determine that the triangles are congruent by the indicated theorem. 11. SSS 78

87 12. SAS 13. ASA 14. AAS For questions 15-22, give the triangle congruence statement and the theorem used to prove they are congruent. If the triangles are not congruent, write not congruent

88 M is the midpoint of PN and LO

89 Multiple Choice Test Solve for x in the following diagrams (a) 67 (b) 63 (c) 35 (d) (a) 75 (b) 68 (c) 67 (d) (a) 69 (b) 62 (c) 58 (d)

90 5. (a) 62 (b) 52 (c) 58 (d) (a) 42 (b) 38 (c) 35 (d) (a) 40 (b) 35 (c) 45 (d) (a) 7 (b) 63 (c) 8 (d) 9 (a) 23 (b) 22 (c)

91 9. (d) (a) 13 (b) 14 (c) 15 (d) 16 (a) 9 (b) 11 (c) 10 (d) 12 For questions 11-18, decide whether the triangles are congruent and if so chose the correct congruence statement and reason (a) ABC DEF by SSS (b) ABC EFD by SSS (c) ABC EDF by SSS (d) not congruent 83

92 13. (a) ABC LMN by SAS (b) ABC LNM by ASA (c) ABC LMN by ASA (d) not congruent 14. (a) S TU QPR by ASA (b) S TU QPR by AAS (c) S TU PQR by AAS (d) not congruent 15. (a) WXZ YZX by SAS (b) WXZ YZX by AAS (c) WXZ YXZ by AAS (d) not congruent 16. (a) ABD DBC by HL (b) ABD CBD by SAS (c) ABD CBD by HL (d) not congruent 84

93 17. (a) PON LOM by SAS (b) PON MOL by SAS (c) PON MOL by AAS (d) not congruent WY bisects XYZ and XWZ (a) WXY YZW by SAS (b) WXY WZY by SAS (c) WXY WZY by ASA (d) not congruent 18. (a) QRV S RT by AAS (b) QRV S RT by ASA (c) QRV TRS by ASA (d) not congruent 4.12 Answers for Chapter 4 Assessment Quiz 1 A: Sections 1 and 2: Triangle Sums and Congruent Figures V 8. WU Quiz 1 B: Sections 1 and 2: Triangle Sums and Congruent Figures 85

94 U 8. WV Quiz 1 C: Sections 1 and 2: Triangle Sums and Congruent Figures W 8. VU Quiz 2 A: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL 1. AB 2. B 3. CB or AB 4. S LE PLO, by AAS 5. CAT DOG, by HL 6. KIT KET, by SAS 7. OAD DTO, by SAS 8. ABC has AAS and DEF has ASA, they aren t the same 9. SSA is not a congruence theorem, quadrilateral TRAP could be an isosceles trapezoid, not a parallelogram as it appears to be. Quiz 2 B: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL 1. CB 2. C 3. CB or AC 4. CAT DOG, by HL 5. S LE PLO, by AAS 6. KIT KET, by SAS 7. OAD DTO, by SAS 86

95 8. SSA is not a congruence theorem, quadrilateral TRAP could be an isosceles trapezoid, not a parallelogram as it appears to be. 9. ABC has AAS and DEF has ASA, they aren t the same Quiz 2 C: Sections 3 and 4: Triangle Congruence SSS, SAS, ASA, AAS and HL 1. AC 2. A 3. CA or AB 4. OAD DTO, by SAS 5. KIT KET, by SAS 6. S LE PLO, by AAS 7. CAT DOG, by HL 8. ABC has AAS and DEF has ASA, they aren t the same 9. SSA is not a congruence theorem, quadrilateral TRAP could be an isosceles trapezoid, not a parallelogram as it appears to be. Quiz 3 A: Section 5: Isosceles and Equilateral Triangles 1. AC 2. C 3. CAE 4. EC 5. RC Quiz 3 B: Section 5: Isosceles and Equilateral Triangles 1. EC 2. RC 3. CAE 4. AC 5. C Quiz 3 C: Section 5: Isosceles and Equilateral Triangles 1. EC 87

96 2. RC 3. CAE 4. C 5. AC Free Response Test DF AB 12. E C 13. UV ZX 14. WV ZY or WU YX 15. S NO S WO, by SAS 16. HAS PAE, by ASA or AAS 17. LMP OMN, by SAS 18. WAE VAE, by HL 19. WVU YZX, by AAS 20. DFE ABC, by SSS 21. Not congruent 22. RFO GOF, by SAS Multiple Choice Test 1. a 2. c 3. d 4. b 5. b 6. a 7. d 8. a 9. c 10. b 11. b 88

97 12. b 13. c 14. a 15. c 16. b 17. c 18. d 89

98 Chapter 5 Relationships with Triangles Assessment:Chapter Quiz 1 A: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles Find the values of the variables in the diagram below. 1. w = 2. x = 3. y = 4. z = Solve for the variables in the diagrams for questions

99 Fill in the blanks with perpendicular bisectors or angle bisectors. 9. The point of intersection of the three is the point equidistant from the three vertices of a triangle. 10. The point of intersection of the three is the point equidistant from the three sides of a triangle. 5.2 Quiz 1 B: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles Find the values of the variables in the diagram below. 1. w = 2. x = 3. y = 91

100 4. z = Solve for the variables in the diagrams for questions Fill in the blanks with perpendicular bisectors or angle bisectors. 9. The point of intersection of the three is the point equidistant from the three sides of a triangle. 10. The point of intersection of the three is the point equidistant from the three vertices of a triangle. 5.3 Quiz 1 C: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angle Bisectors in Triangles Find the values of the variables in the diagram below. 92

101 1. w = 2. x = 3. y = 4. z = Solve for the variables in the diagrams for questions Fill in the blanks with perpendicular bisectors or angle bisectors. 9. The point of intersection of the three is the point equidistant from the three vertices of a triangle. 93

102 10. The point of intersection of the three is the point equidistant from the three sides of a triangle. 5.4 Quiz 2 A: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Use the diagram to fill the blanks below. 1. Identify an altitude in the triangle. 2. Identify a median in the triangle. 3. Identify the centroid in the triangle. 4. EG is half the length of. 5. is three times the length of FG. In the diagram below L, M and N are midpoints of AB, CB and AC respectively. 6. If NO = 8, then OB =. 7. If CO = 14, then LO =. 8. If AM = 18, then OM = and AO =. 9. If CB = 30, then MB =. 10. If NA = 17, then CA =. In questions 11 and 12, list the variables a, b and c in order from least to greatest. 94

103 For questions 14-16, decide whether a is <, > or = to b Give three lengths that could make a triangle. 18. If two sides of a triangle have lengths 5 and 12, what are the possible lengths of the third side? 95

104 5.5 Quiz 2 B: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Use the diagram to fill the blanks below. 1. Identify a median in the triangle. 2. Identify the centroid in the triangle. 3. Identify an altitude in the triangle. 4. FG is half the length of. 5. is three times the length of EG. In the diagram below L, M and N are midpoints of AB, CB and AC respectively. 6. If NO = 7, then OB =. 7. If CO = 16, then LO =. 8. If AM = 21, then OM = and AO =. 9. If CB = 32, then MB =. 10. If NA = 19, then CA =. In questions 11 and 12, list the variables a, b and c in order from least to greatest

105 For questions 14-16, decide whether a is <, > or = to b Give three lengths that could make a triangle. 18. If two sides of a triangle have lengths 6 and 12, what are the possible lengths of the third side? 5.6 Quiz 2 C: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles Use the diagram to fill the blanks below. 97

106 1. Identify the centroid in the triangle. 2. EG is half the length of. 3. Identify an altitude in the triangle. 4. is three times the length of FG. 5. Identify a median in the triangle. In the diagram below L, M and N are midpoints of AB, CB and AC respectively. 6. If NO = 6, then OB =. 7. If CO = 12, then LO =. 8. If AM = 15, then OM = and AO =. 9. If CB = 28, then MB =. 10. If NA = 18, then CA =. In questions 11 and 12, list the variables a, b and c in order from least to greatest

107 13. For questions 14-16, decide whether a is <, > or = to b Give three lengths that could make a triangle. 18. If two sides of a triangle have lengths 5 and 17, what are the possible lengths of the third side? 5.7 Quiz 3: Extension: Indirect Proof 1. Put the steps of an indirect proof in order. Use logical reasoning laws (Law of Detachment, Law of Syllogism, Law of Contrapositive) to make valid conclusions State that your conjecture must be true Reach a contradiction Determine that what you assumed must be false Assume the opposite of the conjecture 2. Fill in the blanks in the Indirect Proof below. Given that Tommy is older than Ellie and Elizabeth is younger than Ellie, prove that Elizabeth is younger than Tommy. Assume that Elizabeth is not younger than. Then, since Tommy is older than, then Elizabeth is older than. This contradicts the fact that is younger than Ellie. Therefore, what we assumed is false and Elizabeth must be younger than. Prove the following Statements true indirectly. 99

108 3. In XYZ, if < X is an obtuse angle then < Y cannot be a right angle. 4. If 11x , then x If a collection of dimes and nickels is worth $0.95, then the collection must contain an odd number of nickels. 5.8 Free Response Test Fill in the blanks to make true statements. 1. A in a triangle is a segment which connects the midpoints of adjacent sides. 2. An altitude in a triangle passes through a vertex and is to the opposite side. 3. Every point on a(n) is equidistant from the sides of the angle. 4. A passes through the midpoint of a segment. 5. The medians of a triangle connect each vertex with the of the opposite side. 6. The centroid is the point of intersections of the. 7. The sum of the lengths of any two sides in a triangle must be than the length of the third side. 8. The distance from the vertex to the centroid is the distance from the centroid to the midpoint of the opposite side. 9. The point equidistant from the vertices of the triangle is the point of intersection of the of the triangle. 10. The midsegment in a triangle is to and the length of the third side. Use ABC with A(2, 6), B(0, 6) and C( 8, 2) to find the equations in questions Find the equation of the line containing the altitude through vertex B. 12. Find the equation of the line containing the midsegment connecting BC and AC. 13. Find the equation of the line containing the median through vertex C. 14. Find the equation of the perpendicular bisector of AB. Solve for the variable(s) in the diagrams for questions

109 17. Use the diagram below for questions If AE = 39, then AF =. 19. If DE = 5x 3 and AB = 9x, find x. 20. If BF = 14, then FD =. Find the value of x in the diagrams in questions 21 and Order the variables from least to greatest in questions 24 and

110 Decide whether the given lengths can form a triangle , 5, , 2, , 24, What are the possible values for the length of the third side if two sides of a triangle are 42 and 76 units? 30. Decide whether a is <, > or = to b in the diagram Multiple Choice Test Fill in the blanks with the correct point. (a) Centroid (b) Midsegment (c) Equidistant (d) Sides 1. In a right triangle, two altitudes are also of the triangle. 2. A is half the length of the third side of the triangle. 3. The perpendicular bisectors of the sides of a triangle are from the vertices. 4. The medians of a triangle intersect at the. 5. The point where the angles bisectors in a triangle intersect is from the sides. 6. The is parallel to a side of the triangle. 7. The center of gravity of a triangle is the. Use ABC with A( 4, 1), B(0, 5) and C(4, 1) to find the equations in questions

111 8. Find the equation of the line containing the altitude through vertex B. (a) y = 4x + 5 (b) y = 1 4 x + 5 (c) y = 4x 5 (d) y = 1 4 x 5 9. Find the equation of the line containing the midsegment connecting BC and AC. (a) y = x (b) y = x + 1 (c) y = x (d) y = x Find the equation of the line containing the median through vertex B. (a) y = 5 (b) x = 5y (c) y = 5x (d) x = Find the equation of the perpendicular bisector of AB. (a) y = x 1 (b) y = x + 1 (c) y = x + 1 (d) y = x 1 Find the value of x in the diagrams (a) 8 (b) 9 (c) 10 (d) 11 (a) 5 (b) 6 (c)

112 14. (d) (a) 7 (b) 8 (c) 9 (d) (a) 5 (b) 6 (c) 7 (d) (a) 4 (b) 3 (c) 5 (d) 6 (a) 5 (b) 2 (c) 3 (d) Which set of three lengths could not make a triangle? 104

113 (a) 2, 3, 4 (b) 10, 10, 20 (c) 5, 7, 11 (d) 21, 33, In ABC, AB = 23 and BC = 42. Which of the following could not be the length of AC. (a) 22 (b) 35 (c) 63 (d) 18 For questions 20-22, fill in the blank x (a) < (b) > (c) = (d) cannot be determined y, with Answers for Chapter 5 Assessment Quiz 1 A: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angles Bisectors in Triangles w = 9 6. y = 7 7. x =

114 8. x = 4 9. perpendicular bisectors 10. angle bisectors Quiz 1 B: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angles Bisectors in Triangles w = y = 5 7. x = x = 3 9. angle bisectors 10. perpendicular bisectors Quiz 1 C: Sections 1 and 2: Midsegments, Perpendicular Bisectors and Angles Bisectors in Triangles w = 8 6. y = 2 7. x = 8 8. x = 5 9. perpendicular bisectors 10. angle bisectors Quiz 2 A: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles 1. BD 2. AF or CE 3. G 4. GC 5. AF , b, c, a 12. c, a, b 13. b, a, c 14. a > b 15. a < b 106

115 16. a = b 17. answers vary < x < 17 Quiz 2 B: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles 1. AF or CE 2. G 3. BD 4. GA 5. EC , b, a, c 12. a, c, b 13. c, a, b 14. a < b 15. a > b 16. a = b 17. answers vary < x < 18 Quiz 2 C: Sections 3 and 4: Medians and Altitudes in Triangles and Inequalities in Triangles 1. G 2. GC 3. BD 4. AF 5. AF or CE , c, a, b 12. b, c, a 13. a, c, b 14. a = b 15. a < b 16. a > b 17. answers vary < x < 22 Quiz 3: Extension: Indirect Proof 1. 2, 5, 3, 4,

116 2. Tommy, Ellie, Ellie, Elizabeth, Tommy 3. Assume Y is a right angle, then X and Z must add up to 90 since the sum of the three angles in a triangles is always 180. Therefore, X must be less than 90. This contradicts the fact that X is obtuse. Therefore, what we assumed is false and Y is not a right angle. 4. Assume x < 3. Then, since 11(3) + 5 = 38, 11x + 5 < 38. This contradicts the fact that 11x Therefore, what we assumed is false and x Assume we have an even number of nickels. An even number of nickels will always be worth a multiple of $0.10. This contradicts the fact that our coin collection is worth $0.95. Therefore, what we assumed is false and we must have an odd number of nickels in our coin collection. Free Response Test 1. midsegment 2. perpendicular 3. angle bisector 4. perpendicular bisector 5. midpoint 6. medians 7. greater 8. twice 9. perpendicular bisectors 10. parallel, half 11. y = 5 4 x y = 6x y = 2 9 x y = 1 6 x x = x = x = x = b, a, c 25. b, c, a 26. no 27. yes 28. yes < x < a < b Multiple Choice Test 1. d 2. b 3. c 4. a 108

117 5. c 6. b 7. a 8. a 9. c 10. d 11. b 12. c 13. b 14. a 15. c 16. a 17. b 18. b 19. d 20. b 21. a 22. c 109

118 Chapter 6 Polygons and Quadrilaterals Assessment:Chapter Quiz 1 A: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms 1. What is the sum of the measures of the angles in a convex 12-gon? 2. What is the measure of each angle in a convex regular 15-gon? 3. If the measure of one exterior angle in a regular polygon is 40, how many sides does the polygon have? 4. How many sides does a convex polygon have if the sum of its interior angles is 1980? 5. If the measure of one interior angle in a regular polygon is 170, what is the measure of one exterior angle? 6. How many sides does the polygon in question 5 have? Find the measures of the numbered angles in the puzzle below. 7. m 1 = 8. m 2 = 9. m 3 = 10. m 4 = 11. m 5 = 12. m 6 = 13. m 7 = For questions, use parallelogram WXYZ

119 14. VY = 15. m VWX = 16. m ZWX = 17. m WXY = 18. ZW = 19. If ZW = 34, XV = 20. Perimeter of WXYZ = 6.2 Quiz 1 B: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms 1. What is the sum of the measures of the angles in a convex 13-gon? 2. What is the measure of each angle in a convex regular 18-gon? 3. If the measure of one exterior angle in a regular polygon is 45, how many sides does the polygon have? 4. How many sides does a convex polygon have if the sum of its interior angles is 1800? 5. If the measure of one interior angle in a regular polygon is 160, what is the measure of one exterior angle? 6. How many sides does the polygon in question 5 have? Find the measures of the numbered angles in the puzzle below. 7. m 1 = 8. m 2 = 9. m 3 = 10. m 4 = 11. m 5 = 12. m 6 = 13. m 7 = For questions, use parallelogram WXYZ

120 14. VY = 15. m VWX = 16. m ZWX = 17. m WXY = 18. ZW = 19. If ZX = 34, XV = 20. Perimeter of WXYZ = 6.3 Quiz 1 C: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms 1. What is the sum of the measures of the angles in a convex 15-gon? 2. What is the measure of each angle in a convex regular 12-gon? 3. If the measure of one exterior angle in a regular polygon is 60, how many sides does the polygon have? 4. How many sides does a convex polygon have if the sum of its interior angles is 2160? 5. If the measure of one interior angle in a regular polygon is 140, what is the measure of one exterior angle? 6. How many sides does the polygon in question 5 have? Find the measures of the numbered angles in the puzzle below. 7. m 1 = 8. m 2 = 9. m 3 = 10. m 4 = 11. m 5 = 12. m 6 = 13. m 7 = For questions, use parallelogram WXYZ

121 14. VY = 15. m VWX = 16. m ZWX = 17. m WXY = 18. ZW = 19. If ZX = 34, XV = 20. Perimeter of WXYZ = 6.4 Quiz 2 A: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares For questions 1-3, determine what values of x and y would make the quadrilaterals parallelograms Use quadrilateral ABCD with vertices A( 2, 6), B(4, 3), C(2, 1) and D( 4, 2) for questions You should plot the points on the given grid to support your work

122 4. Find the midpoint of diagonal AC. 5. Find the midpoint of diagonal BD. 6. What do your answers to 4 and 5 tell us about the diagonals of quadrilateral ABCD? 7. Find the length of AC. 8. Find the length of BD. 9. Find the slopes of AC and BD. 10. Is quadrilateral ABCD a rectangle, rhombus or square? How do you know? Use only the given markings in the diagrams to determine whether each figure is a rectangle rhombus or square

123 Quiz 2 B: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares For questions 1-3, determine what values of x and y would make the quadrilaterals parallelograms Use quadrilateral ABCD with vertices A(1, 7), B(5, 4), C(2, 0) and D( 2, 3) for questions You should plot the points on the given grid to support your work

124 4. Find the midpoint of diagonal AC. 5. Find the midpoint of diagonal BD. 6. What do your answers to 4 and 5 tell us about the diagonals of quadrilateral ABCD? 7. Find the length of AC. 8. Find the length of BD. 9. Find the slopes of AC and BD. 10. Is quadrilateral ABCD a rectangle, rhombus or square? How do you know? Use only the given markings in the diagrams to determine whether each figure is a rectangle rhombus or square

125 Quiz 2 C: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares For questions 1-3, determine what values of x and y would make the quadrilaterals parallelograms Use quadrilateral ABCD with vertices A( 4, 4), B(0, 6), C(4, 4) and D(0, 2) for questions You should plot the points on the given grid to support your work

126 4. Find the midpoint of diagonal AC. 5. Find the midpoint of diagonal BD. 6. What do your answers to 4 and 5 tell us about the diagonals of quadrilateral ABCD? 7. Find the length of AC. 8. Find the length of BD. 9. Find the slopes of AC and BD. 10. Is quadrilateral ABCD a rectangle, rhombus or square? How do you know? Use only the given markings in the diagrams to determine whether each figure is a rectangle rhombus or square

127 Quiz 3 A: Section 5: Trapezoids and Kites T RAP is an Isosceles trapezoid. 1. If T A = 8, then RP = 2. m T PA = 3. m TRA = 4. m ET P = KIT E is a kite. 5. If IE = 14, then YE = 6. m YIT = 7. m KET = 8. m KIY = Find the value of the variable for questions

128 Quiz 3 B: Section 5: Trapezoids and Kites T RAP is an Isosceles trapezoid. 1. If T A = 8, then RP = 2. m T PA = 3. m TRA = 4. m ET P = KIT E is a kite

129 5. If IE = 14, then YE = 6. m YIT = 7. m KET = 8. m KIY = Find the value of the variable for questions Quiz 3 C: Section 5: Trapezoids and Kites T RAP is an Isosceles trapezoid. 1. If T A = 8, then RP = 2. m T PA = 121

130 3. m TRA = 4. m ET P = KIT E is a kite. 5. If IE = 14, then YE = 6. m YIT = 7. m KET = 8. m KIY = Find the value of the variable for questions

131 6.10 Free Response Test Fill in the blanks below. 1. The formula gives the sum of the angles in a convex polygon. 2. The sum of the exterior angles of a convex polygon is. 3. The diagonals in a parallelogram each other. 4. The diagonals of a rectangle are. 5. A quadrilateral with all sides congruent is a. 6. The diagonals of an trapezoid are congruent. 7. Exactly one diagonal is a perpendicular bisector of the other in a. 8. The midsegment of a trapezoid is to the bases. 9. The measure of each angle in a regular octagon is. 10. If the measure of each angle in a regular polygon is 165, then it has sides. PARG is a parallelogram. 11. PR = 12. m PGR = 13. m APG = 14. GR = 15. If perimeter of PARG is 72, AR = RECT is a rectangle. 16. m RCE = 17. m ETC = 18. x = 19. y = 20. z = RHOM is a rhombus

132 21. m RS H = 22. m ROH = 23. x = 24. Perimeter of RHOM = 25. If MH = 24, then S H = S QAR is a square. 26. Name the segments congruent to EQ. 27. Name the segments congruent to QA. 28. m S AQ = 29. m RAQ = 30. m QEA = KIT E is a kite

133 31. x = 32. y = 33. z = 34. m KIS = 35. m ET I = MDS G is a trapezoid. 36. x = 37. y = 38. z = 6.11 Multiple Choice Test You may wish to plot the quadrilaterals in problems 1-6 to help you answer the questions. For questions 1 & 2, use the quadrilateral QUAD with vertices Q( 3, 1), U(1, 6), A(6, 4) and D(2, 3). 1. Find the slopes and midpoints of QA and UD to make a conclusion about the diagonals. (a) perpendicular, bisector each other (b) bisect each other (c) perpendicular (d) one diagonal bisects the other 2. Use your answer from question 1 to classify the quadrilateral QUAD. (a) parallelogram (b) square (c) rhombus (d) kite For questions 3 & 4, use the quadrilateral LIME with vertices L( 5, 3), I( 2, 3), M(2, 1) and E( 1, 5). 3. Use the midpoints, slopes and lengths of the diagonals LM and IE to make a conclusion. (a) diagonals are congruent (b) diagonals are perpendicular and congruent (c) diagonals are congruent and bisect each other (d) bisect each other 4. Use your answer from question 3 to classify the quadrilateral LIME. (a) parallelogram (b) rhombus (c) rectangle 125

134 (d) kite For questions 5 & 6, use the quadrilateral ROS E with vertices R(6, 5), O(3, 1), S ( 2, 1), E(1, 5). 5. Use the midpoints, slopes and lengths of the diagonals RS and OE make a conclusion. (a) diagonals are perpendicular bisectors of each other (b) diagonals are congruent (c) diagonals are congruent and bisect each other (d) bisect each other 6. Use your answer from question 5 to classify the quadrilateral ROS E. (a) parallelogram (b) rhombus (c) rectangle (d) kite 7. If diagonals are congruent, perpendicular bisectors of one another, the quadrilateral is a. (a) kite (b) parallelogram (c) rhombus (d) square 8. A quadrilateral in which exactly one diagonal perpendicularly bisects the other is a. (a) rhombus (b) square (c) trapezoid (d) kite 9. A quadrilateral with exactly one pair of parallel sides is a. (a) parallelogram (b) square (c) trapezoid (d) kite 10. If the measure of one interior angle of a regular polygon is 150, the polygon has sides. (a) 10 (b) 12 (c) 14 (d) 8 For questions 11-14, fill in the blanks in the proof with the answers. Given: T RAP is an isosceles trapezoid Prove: T A RP (a) definition of isosceles trapezoid 126

135 (b) CPCTC (c) SAS (d) base angles congruent in isosceles trapezoid Statements Table 6.1: Reasons T RAP is an isosceles trapezoid Given T P RA 11. PA PA Reflexive RAP T PA 12. T AP RPA 13. RP T A 14. Use the markings in the diagram to classify the quadrilaterals. Give the most specific classification (a) parallelogram (b) trapezoid (c) rhombus (d) kite 17. (a) square (b) parallelogram (c) rectangle (d) rhombus (a) parallelogram (b) rectangle (c) square (d) rhombus 127

136 (a) quadrilateral (b) trapezoid (c) rhombus (d) kite 20. (a) kite (b) isosceles trapezoid (c) trapezoid (d) parallelogram (a) square (b) rectangle (c) rhombus (d) parallelogram 6.12 Answers for Chapter 6 Assessment Quiz 1 A: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms

137 Quiz 1 B: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms Quiz 1 C: Sections 1 and 2: Angles in Polygons and Properties of Parallelograms

138 Quiz 2 A: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares 1. x = 29, y = x = 19, y = 4 3. x = 7, y = ( ) 0, ( ) 0, They bisect each other slope of AC = 7 4 ; slope of BD = rectangle, the diagonals are congruent 11. rectangle 12. rhombus 13. square Quiz 2 B: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares 1. x = 35, y = x = 15, y = 3 3. x = 6, y = ( 3 2, ) ( 3 2, ) They bisect each other = = slope of AC = 7; slope of BD = square, the diagonals are congruent and perpendicular 11. rhombus 12. rectangle 13. square Quiz 2 C: Sections 3 and 4: Proving Quadrilaterals are Parallelograms, Rectangles, Rhombuses and Squares 1. x = 27, y =

139 2. x = 17, y = 5 3. x = 8, y = (0, 4) 5. (0, 4) 6. They bisect each other slope of AC = 0; slope of BD is undefined 10. rhombus, the diagonals are perpendicular 11. square 12. rhombus 13. rectangle Quiz 3 A: Section 5: Trapezoids and Kites x = x = x = y = 7 Quiz 3 B: Section 5: Trapezoids and Kites x = x = x = y = 8 Quiz 3 C: Section 5: Trapezoids and Kites

140 x = x = x = y = 9 Free Response Test 1. (n 2) bisect 4. congruent 5. rhombus 6. isosceles 7. kite 8. parallel ES.EA, ER 27. AR, RS, S Q

141 Multiple Choice Test 1. b 2. a 3. c 4. c 5. a 6. b 7. d 8. d 9. c 10. b 11. a 12. b 13. c 14. b 15. b 16. c 17. d 18. d 19. b 20. a 133

142 Chapter 7 Similarity Assessment:Chapter Quiz 1 A: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. In a Geometry class there are 12 girls and 15 boys. What is the ratio of girls to the total number of students in the class? Reduce your answer if possible. 2. On a school s swim team the ratio of boys to girls is 7 to 5. If there are 60 swimmers on the team, how many of them are girls? Solve the following proportions = 35 x = 10 x+1 y+2 12 = y The measures of the angles in a triangle are in the ratio 2:4:9. Find the measure of the angles. 7. The length and width of a rectangle are in the ratio 7:12. Given that the perimeter of the rectangle is 114 cm. Find the dimensions of the rectangle. 8. Corey used 14 gallons of gas to drive 336 miles. How many miles could she drive with 18 gallons of gas? In the picture, AB BC = AE ED and EB DC = AB AC. Use these proportions for questions 9 and Find BC. 10. Find EB

143 Use the picture below in which ABCDE FGHJK to answer questions Find m C 12. Find m K 13. What is the scale factor? 14. Find CD. 15. Find BC. 16. Find FK. 7.2 Quiz 1 B: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. In a Geometry class there are 13 girls and 15 boys. What is the ratio of girls to the total number of students in the class? Reduce your answer if possible. 2. On a school s swim team the ratio of boys to girls is 7 to 5. If there are 72 swimmers on the team, how many of them are girls? Solve the following proportions = 30 x = 15 x+1 y+2 12 = y The measures of the angles in a triangle are in the ratio 4:5:9. Find the measure of the angles. 7. The length and width of a rectangle are in the ratio 7:12. Given that the perimeter of the rectangle is 133 cm. Find the dimensions of the rectangle. 8. Corey used 14 gallons of gas to drive 350 miles. How many miles could she drive with 18 gallons of gas? In the picture, AB BC = AE ED and EB DC = AB AC. Use these proportions for questions 9 and Find BC. 10. Find EB. Use the picture below in which ABCDE FGHJK to answer questions

144 11. Find m C 12. Find m K 13. What is the scale factor? 14. Find CD. 15. Find BC. 16. Find FK. 7.3 Quiz 1 C: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. In a Geometry class there are 12 girls and 18 boys. What is the ratio of girls to the total number of students in the class? Reduce your answer if possible. 2. On a school s swim team the ratio of boys to girls is 7 to 5. If there are 84 swimmers on the team, how many of them are girls? Solve the following proportions = 40 x = 20 x+1 y 9 11 = y The measures of the angles in a triangle are in the ratio 3:5:7. Find the measure of the angles. 7. The length and width of a rectangle are in the ratio 7:12. Given that the perimeter of the rectangle is 152 cm. Find the dimensions of the rectangle. 8. Corey used 14 gallons of gas to drive 364 miles. How many miles could she drive with 18 gallons of gas? In the picture, AB BC = AE ED and EB DC = AB AC. Use these proportions for questions 9 and Find BC. 10. Find EB. Use the picture below in which ABCDE FGHJK to answer questions

145 11. Find m C 12. Find m K 13. What is the scale factor? 14. Find CD. 15. Find BC. 16. Find FK. 7.4 Quiz 2 A: Sections 3 and 4: Similarity by AA, SSS and SAS Fill in the blanks. 1. The three triangle similarity theorems are, and. 2. The corresponding sides in similar triangles are. 3. The corresponding angles in similar triangles are. In questions 4-7, determine whether the triangles are similar. If they are similar, write the triangle similarity statement and give the similarity theorem

146 7. Solve for the variables below. If not enough information is given, write cannot be determined Use similar triangles to solve the word problem. Round your answer to the nearest tenth. 10. Jonathan wants to measure the height of a tree in his yard. The tree casts a 28 ft shadow at the same time his 5.5 ft frame casts an 8 ft shadow. 7.5 Quiz 2 B: Sections 3 and 4: Similarity by AA, SSS and SAS Fill in the blanks. 1. The corresponding angles in similar triangles are. 2. The corresponding sides in similar triangles are. 3. The three triangle similarity theorems are, and. In questions 4-7, determine whether the triangles are similar. If they are similar, write the triangle similarity statement and give the similarity theorem

147 Solve for the variables below. If not enough information is given, write cannot be determined Use similar triangles to solve the word problem. Round your answer to the nearest tenth. 10. Jonathan wants to measure the height of a tree in his yard. The tree casts a 36 ft shadow at the same time his 5.7 ft frame casts an 9 ft shadow. 7.6 Quiz 2 C: Sections 3 and 4: Similarity by AA, SSS and SAS Fill in the blanks

148 1. The corresponding sides in similar triangles are. 2. The three triangle similarity theorems are, and. 3. The corresponding angles in similar triangles are. In questions 4-7, determine whether the triangles are similar. If they are similar, write the triangle similarity statement and give the similarity theorem Solve for the variables below. If not enough information is given, write cannot be determined

149 Use similar triangles to solve the word problem. Round your answer to the nearest tenth. 10. Jonathan wants to measure the height of a tree in his yard. The tree casts a 48 ft shadow at the same time his 5.6 ft frame casts an 14 ft shadow. 7.7 Quiz 3 A: Sections 5 and 6: Proportionality Relationships and Similarity Transformations Find the value of x Find the values of x and y below

150 Find the scale factor and the values of the variables in each of the dilations below The black figure is the original. AEFG is the dilation of ABCD. 8. Plot the triangle with vertices (2, 2), (4, 0) and (2, 4) on the grid below. 9. Plot the triangle with vertices (3, 3), (6, 0) and (3, 6). 10. The triangle in question 9 is a dilation centered at zero of the triangle in question 8. What is the scale factor of this dilation? 7.8 Quiz 3 B: Sections 5 and 6: Proportionality Relationships and Similarity Transformations Find the value of x

151 Find the values of x and y below Find the scale factor and the values of the variables in each of the dilations below. 6. The black figure is the original

152 7. AEFG is the dilation of ABCD. 8. Plot the triangle with vertices (2, 2), (4, 0) and (2, 4) on the grid below. 9. Plot the triangle with vertices (3, 3), (6, 0) and (3, 6). 10. The triangle in question 8 is a dilation centered at zero of the triangle in question 9. What is the scale factor of this dilation? 7.9 Quiz 3 C: Sections 5 and 6: Proportionality Relationships and Similarity Transformations Find the value of x

153 3. Find the values of x and y below Find the scale factor and the values of the variables in each of the dilations below The black figure is the original. AEFG is the dilation of ABCD. 8. Plot the triangle with vertices (0, 2), (2, 0) and (4, 4) on the grid below. 9. Plot the triangle with vertices (0, 3), (3, 0) and (6, 6). 10. The triangle in question 9 is a dilation centered at zero of the triangle in question 8. What is the scale factor of this dilation? 145

154 7.10 Quiz 4: Extension: Self-Similarity 1. What is the first step of a fractal called? 2. A variation on the Koch Snowflake is a pentagon fractal snowflake. The first three steps are below. Describe the fourth step and then draw it as best you can. 3. A table of the number of purple pentagons is below. Fill in the missing entries as well as the missing step numbers. Table 7.1: Purple Pentagons Describe the fifth step of this fractal. How many purple pentagons should it have? Does this match your answer from #3? 5. Describe the pattern for the number of purple pentagons in the fractal Free Response Test 1. The yearbook club has 32 members. The ratio of girls to boys is 3:1. How many boys are in the club? 2. The angles in a triangle are in the ratio 5:7:8. What are the angle measures? Use the figure below and the proportions LP PO = LM MN LP and LO = PM ON for questions 3-10.

155 3. LP = 4. ON = 5. Perimeter of LNO = For questions 8-12, use ABCD WXYZ. 6. m X = 7. WX = 8. XY = 9. WZ = 10. Perimeter of ABCD = In questions 11-14, determine whether the triangles are similar. If they are similar, write the triangle similarity statement and give the similarity theorem

156 Solve for the variables. w = x = y = z = 16. Marco stands near a flagpole and measures his shadow to be 15 ft and the flagpole s shadow to be 30 ft. If Marco is 5.8 ft tall, how tall is the flagpole? 17. Solve for x and y in the figure below. 18. Solve for x in the figure below. 19. Give the scale factor for the dilation below and find x. The black figure is the original figure Multiple Choice Test 1. The ratio of length to width in a rectangle is 5:9 and its perimeter is 196 cm. What are the dimensions of the rectangle? (a) 25 by

157 (b) 30 by 68 (c) 35 by 63 (d) 40 by A recipe calls for cups flour to make 2 dozen cookies. If we need to make 3 dozen cookies, how much flour will we need? (a) 2 cups (b) cups (c) cups (d) cups 3. Which of the following statements is not true given that LPM LON. (a) LP PO = LM MN (b) LM LN = LP LO (c) PM ON = LM LN (d) LM MN = PM ON 4. Which statement is false? (a) All rhombuses are similar. (b) All regular pentagons are similar. (c) All squares are regular. (d) All equilateral triangles are similar. 5. Given the proportion: a b = c d, identify the proportion which is not equivalent. (a) a c = b d (b) a+b b (c) b a = d c (d) a c = d b = c+d d For questions 6-10, fill in the blanks with one of the following choices. (a) congruent (b) proportional (c) similar (d) regular 6. The sides of similar polygons are. 7. Angles in similar polygons are. 8. If two angles in one triangle are congruent to two angles in another triangle, the triangles are polygons are always congruent. 10. If all three sides in one triangle are proportional to all three sides in a second triangle, the triangles are

158 11. Find the values of x and y in the diagram below. ABCDE LMNOP (a) x = 6, y = 9 (b) x = 9, y = 16 (c) x = 8, y = 19 (d) x = 9, y = Solve for the variables in the diagram below. (a) x = 7, y = 23 (b) x = 6, y = 21 (c) x = 8, y = 22 (d) x = 5, y = Solve for x in the diagram below. (a) x = 13 (b) x = 12 (c) x = 7 (d) x = Find the scale factor for the dilation and find x

159 (a) scale factor 3 2, x = 6 (b) scale factor 9 5, x = 5 (c) scale factor 3 1, x = 3 (d) scale factor 9 4, x = Roberto wants to find the height of his apartment building. He measures his shadow length and the length of the shadow of the building. Given that his height is 5.8 ft, the length of his shadow is 12 ft and the building s shadow is 108 ft long, how tall is the apartment building. (a) 34.8 ft (b) 29 ft (c) 46.4 ft (d) 52.2 ft 7.13 Answers for Chapter 7 Assessment Quiz 1 A: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. 4: x = x = y = , 48, by miles Quiz 1 B: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. 13: x = x = y = , 50, by miles

160 Quiz 1 C: Sections 1 and 2: Ratios and Proportions and Similar Polygons 1. 2: x = x = y = , 60, by miles Quiz 2 A: Sections 3 and 4: Similarity by AA, SSS and SAS 1. SSS, SAS, AA 2. proportional 3. congruent 4. FJK HJG by AA 5. ABC DEF by SAS 6. LPM LON by AA 7. PQR S TU by SSS 8. x = 6, y = 14, z = x = 65, y = 65, z = ft Quiz 2 B: Sections 3 and 4: Similarity by AA, SSS and SAS 1. congruent 2. proportional 3. SSS, SAS, AA 4. ABC DEF by SAS 5. FJK HJG by AA 6. PQR S TU by SSS 7. LPM LON by AA 8. x = 3, y = 10, z = x = 63, y = 63, z = ft 152

161 Quiz 2 C: Sections 3 and 4: Similarity by AA, SSS and SAS 1. proportional 2. SSS, SAS, AA 3. congruent 4. LPM LON by AA 5. PQR S TU by SSS 6. ABC DEF by SAS 7. FJK HJG by AA 8. x = 9, y = 22, z = x = 66, y = 66, z = ft Quiz 3 A: Sections 5 and 6: Proportionality Relationships and Similarity Transformations 1. x = 3 2. x = 8 3. x = 4 4. x = 3, y = 3 5. x = 2.5, y = 2 6. x = 6 7. x = 12 8 and 9. The graph is below Quiz 3 B: Sections 5 and 6: Proportionality Relationships and Similarity Transformations 1. x = 2 2. x = 9 3. x = 7 4. x = 2.5, y = x = 3, y = 3 6. x = 6 7. x = and 9. The graph is below

162 Quiz 3 C: Sections 5 and 6: Proportionality Relationships and Similarity Transformations 1. x = 6 2. x = x = x = 3, y = 3 5. x = 2.5, y = 2 6. x = 9 7. x = 8 8 and 9. The graph is below Quiz 4: Extension: Self-Similarity 1. Stage Stage 0, Stage 1, Stage 2, Stage 3, Stage 4, Stage 5 0, 1, 6, 31, 156, The fifth step will have 156 purple pentagons. Yes, it should be the same as Stage 4 in #3. 5. The pattern increase by a power of 5 each time. First add 1, then add 5, add 25, add 125, add 625. Free Response Test 154

163 , 63, ABE DBC by AA 12. CAT DOG by SSS 13. QUR QTS by AA 14. LMN PQR by SAS 15. w = 14, x = 52, y = 38, z = ft 17. x = 4, y = x = x = 15 Multiple Choice Test 1. c 2. b 3. d 4. a 5. d 6. b 7. a 8. c 9. d 10. c 11. d 12. a 13. d 14. d 15. d 155

164 Chapter 8 Right Triangle Trigonometry Assessment:Chapter Quiz 1 A: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Simplify the following radical expressions ( 7 2 ) Use the Pythagorean Theorem to find the unknown length in the diagrams below

165 10. Is 9, 40, 41 a Pythagorean Triple? 11. Name two unique Pythagorean Triples:, 12. Find the distance between the points (2, -8) and (14, 8). Determine whether the following lengths form a right, acute or obtuse triangle , 21 and , 8 and , 7 and Quiz 1 B: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Simplify the following radical expressions ( 7 3 ) Use the Pythagorean Theorem to find the unknown length in the diagrams below Is 15, 36, 39 a Pythagorean Triple? 11. Name two unique Pythagorean Triples:, 12. Find the distance between the points (2, -8) and (7, 4). Determine whether the following lengths form a right, acute or obtuse triangle

166 13. 20, 23 and , 30 and , 7 and Quiz 1 C: Sections 1 and 2: The Pythagorean Theorem, its Converse and the Distance Formula Simplify the following radical expressions ( 4 5 ) Use the Pythagorean Theorem to find the unknown length in the diagrams below Is 14, 48, 50 a Pythagorean Triple? 11. Name two unique Pythagorean Triples:, 12. Find the distance between the points (2, -7) and (10, 8). Determine whether the following lengths form a right, acute or obtuse triangle , 18 and , 9 and , 40 and

167 8.4 Quiz 2 A: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Find the geometric mean of the following pairs of numbers. Reduce any radicals and and and Use the diagram to the right to answer the following questions. (a) Draw and label the three separate similar triangles. (b) Complete the similarity statement: ABC (c) x = (d) y = (e) z = Solve for the variables in the following diagrams

168 8. 9. A side in a square is 7 2 inches. What is the length of the diagonal? 10. The perimeter of an equilateral triangle is 48 cm. Find the length of an altitude. 8.5 Quiz 2 B: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Find the geometric mean of the following pairs of numbers. Reduce any radicals and and and Use the diagram to the right to answer the following questions. (a) Draw and label the three separate similar triangles. (b) Complete the similarity statement: ABC (c) x = (d) y = (e) z = Solve for the variables in the following diagrams

169 A side in a square is 9 2 inches. What is the length of the diagonal? 10. The perimeter of an equilateral triangle is 54 cm. Find the length of an altitude. 8.6 Quiz 2 C: Sections 3 and 4: Similar Right Triangles and Special Right Triangles Find the geometric mean of the following pairs of numbers. Reduce any radicals and and and Use the diagram to the right to answer the following questions. (a) Draw and label the three separate similar triangles. (b) Complete the similarity statement: ABC 161

170 (c) x = (d) y = (e) z = Solve for the variables in the following diagrams A side in a square is 5 2 inches. What is the length of the diagonal? 10. The perimeter of an equilateral triangle is 60 cm. Find the length of an altitude. 8.7 Quiz 3 A: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. Find the sine, cosine and tangent of B. Leave answers in fraction form

171 sin B = cos B = tan B = For problems 2-4, use your calculator to find the ratios. Round answers to four decimal places. 2. sin cos tan 65 For problems 5-7, solve for x and y using trigonometric ratios. Round answers to nearest tenth For problems 8-10, solve the right triangles by finding x, y and z. Round lengths to the nearest hundredth and angles to the nearest degree

172 For questions 11 and 12, you may wish to draw a picture to illustrate the scenario and solve. 11. The angle of depression from the roof of a 105 ft tall apartment building to the base of a fountain in the courtyard in 32. To the nearest foot, how far away from the building is the fountain? 12. A 50 ft tower casts a 65 ft shadow. To the nearest degree, what is the angle at which the sun hits the tower? 8.8 Quiz 3 B: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. Find the sine, cosine and tangent of B. Leave answers in fraction form. sin B = cos B = tan B = For problems 2-4, use your calculator to find the ratios. Round answers to four decimal places. 2. sin cos tan 61 For problems 5-7, solve for x and y using trigonometric ratios. Round answers to nearest tenth

173 6. 7. For problems 8-10, solve the right triangles by finding x, y and z. Round lengths to the nearest hundredth and angles to the nearest degree For questions 11 and 12, you may wish to draw a picture to illustrate the scenario and solve. 11. The angle of depression from the roof of a 115 ft tall apartment building to the base of a fountain in the courtyard in 36. To the nearest foot, how far away from the building is the fountain? 12. A 55 ft tower casts a 45 ft shadow. To the nearest degree, what is the angle at which the sun hits the tower? 165

174 8.9 Quiz 3 C: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. Find the sine, cosine and tangent of B. Leave answers in fraction form. sin B = cos B = tan B = For problems 2-4, use your calculator to find the ratios. Round answers to four decimal places. 2. sin cos tan 60 For problems 5-7, solve for x and y using trigonometric ratios. Round to the nearest tenth For problems 8-10, solve the right triangles by finding x, y and z. Round lengths to the nearest hundredth and angles to the nearest degree

175 For questions 11 and 12, you may wish to draw a picture to illustrate the scenario and solve. 11. The angle of depression from the roof of a 125 ft tall apartment building to the base of a fountain in the courtyard in 38. To the nearest foot, how far away from the building is the fountain? 12. A 58 ft tower casts a 62 ft shadow. To the nearest degree, what is the angle at which the sun hits the tower? 8.10 Free Response Test Simplify the following radical expressions ( 3 5 ) 2 Use the Pythagorean Theorem to find the unknown length in the diagrams below to the nearest hundredth

176 Find the distance between the points (-10, 3) and (-3, 27) Determine whether the following lengths form a right, acute or obtuse triangle , 15, , 13, , 42, What is the geometric mean of 5 and 35? Leave your answer in reduced radical form. Solve for the variables in the following diagrams. Reduce any radicals x = y = z = The length of a diagonal in a square is 8 cm. What is the length of a side? 16. The length of the altitude in an equilateral triangle is What is the length of a side? Use your calculator to find the following trig ratios. Round your answers to four decimal places

177 17. cos tan sin 75 Given the trigonometric ratio, find the measure of the angle. Round your answer to the nearest degree. 20. tan A , A 21. sin A , A 22. cos A , A Solve for the variables in the diagrams below. Round lengths to the nearest tenth and angles to the nearest degree Veronica measures the angle of elevation to the top of a building from her eye level (5 ft above the ground) to be 67 when she is standing 25 ft from the building. How tall is the building? 8.11 Multiple Choice Test 1. Which of the following expressions is not completely reduced. (a)

178 (b) 2 10 (c) (d) For questions 2-5, find the value of the variable(s). Reduce all radical answers (a) a = 10 (b) a = 2 7 (c) a = 14 (d) a = (a) c = 15 (b) c = 353 (c) c = 11 3 (d) c = (a) b = 5 3 (b) b = 5 2 (c) b = 3 5 (d) b = 2 5 (a) c = 9 3 (b) c = 5 9 (c) c = 27 2 (d) c =

179 6. Find the distance between the points (8, 15) and (3, 5). (a) 5 3 (b) 3 3 (c) 3 5 (d) Which of the following is not a Pythagorean Triple? (a) 24, 32, 40 (b) 15, 36, 39 (c) 9, 40, 41 (d) 20, 21, 28 For questions 8-11, decide whether the three lengths form a triangle which is (a) acute (b) obtuse (c) right (d) not a triangle 8. 6, 7 and , 80 and , 2 and , 15 and Which of the following is the geometric mean of 49 and 27? (a) 21 3 (b) 21 (c) 21 2 (d) 21 7 Use the diagram below for questions 13 and Which proportion is not true? (a) 3 x = x 3+y (b) 3 9 = 9 y (c) z y = 3+y z (d) z x = y Solve for x, y and z. (a) x = 10 3, y = 27, z = 9 10 (b) x = 3 10, y = 27, z = 9 10 (c) x = 3 3, y = 27, z =

180 (d) x = 3 10, y = 27 3, z = 9 10 Solve for the variables in the following diagrams (a) x = 16, y = 8 3 (b) x = 16 3, y = 8 (c) x = 16 2, y = 8 3 (d) x = 16, y = 8 2 (a) x = 15 2, y = 15 2 (b) x = 15, y = 15 3 (c) x = 15, y = 15 2 (d) x = 15, y = The sides of a rectangle are in the ratio 14 : Which is the length of the diagonal? (a) 14 6 (b) 28 (c) 28 3 (d) Which is the value of sin 86 rounded to four decimal places? (a) (b) (c) (d) Which of the following is the measure of A if cos A ? (a) 19 (b) 18 (c) 71 (d) 72 Solve for the variable in the following diagrams

181 (a) (b) (c) (d) (a) 9.72 (b) (c) (d) (a) 35.4 (b) 54.6 (c) 45.3 (d) 44.7 (a) 59.9 (b) 30.1 (c)

182 (d) Alfonzo is flying a kite and wants to figure out how high his kite went. When the kite reached its greatest height, Alfonzo determined that he had let out 40 m of kite string and he measured the angle of elevation of the string to be 60. Assuming that Alfonzo is holding the end of the kite string 1 m above ground, how high did his kite get? Answers are rounded to the nearest meter. (a) 21 m (b) 70 m (c) 36 m (d) 24 m 8.12 Answers for Chapter 8 Assessment Quiz 1 A: Sections 1 and 2: Formula The Pythagorean Theorem, its Converse and the Distance yes 11. Any two of: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25; 20, 21, right 14. obtuse 15. acute Quiz 1 B: Sections 1 and 2: Formula The Pythagorean Theorem, its Converse and the Distance yes 11. Any two of: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25; 20, 21, acute 14. right 174

183 15. obtuse Quiz 1 C: Sections 1 and 2: Formula The Pythagorean Theorem, its Converse and the Distance yes 11. Any two of: 3, 4, 5; 5, 12, 13; 8, 15, 17; 7, 24, 25; 20, 21, obtuse 14. acute 15. right Quiz 2 A: Sections 3 and 4: Similar Right Triangles and Special Right Triangles (a) (b) ABC ACD CBD (c) 2 13 (d) 6 (e) x = 4, y = x = 3, y = x = 6, y = x = 3 3, y = Quiz 2 B: Sections 3 and 4: Similar Right Triangles and Special Right Triangles

184 (a) (b) ABC ACD CBD (c) 15 (d) 12 (e) x = 6, y = x = 4, y = x = 15, y = x = 4 3, y = Quiz 2 C: Sections 3 and 4: Similar Right Triangles and Special Right Triangles (a) (b) ABC ACD CBD (c) 3 34 (d) 15 (e) x = 10, y = x = 6, y = x = 12, y = x = 5 3, y = Quiz 3 A: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. sin B = 12 13, cos B = , tan B =

185 5. x = 3.7, y = x = 2.5, y = x = 4.9, y = x = 46, y = 44, z = x = 39, y = 51, z = x = 17, y = 63, z = ft Quiz 3 B: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. sin B = 24 25, cos B = , tan B = x = 4.3, y = x = 2.3, y = x = 5.4, y = x = 25, y = 65, z = x = 54, y = 36, z = x = 29, y = 61, z = ft Quiz 3 C: Sections 5 and 6: Tangent, Sine and Cosine Ratios and Solving Right Triangles 1. sin B = 15 17, cos B = , tan B = x = 4.8, y = x = 3.3, y = x = 7.8, y = x = 22, y = 68, z = x = 46, y = 44, z = x = 34, y = 56, z = ft Free Response Test obtuse 177

186 9. acute 10. Right x = 6 5; y = 12; z = x = ; y = x = 11, y = x = 10.1, y = x = 42.1, y = x = 17, y = 73, z = x = 32, y = 58, z = ft Multiple Choice Test 1. c 2. b 3. b 4. a 5. d 6. a 7. d 8. a 9. c 10. d 11. b 12. a 13. d 14. b 15. a 16. c 17. b 18. a 19. c 20. a 21. c 22. d 23. b 24. c 178

187 Chapter 9 Circles Assessment:Chapter Quiz 1 A: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Use the diagram to match the circle parts with the best description. 1. F J A. common internal tangent 2. GE B. minor arc 3. GH C. diameter 4. BC D. secant 5. BJ E. major arc 6. DB F. common external tangent 7. BC G. radius 8. ĜJH H. chord 9. Find the perimeter of the triangle circumscribed about the circle. 10. Is the segment a tangent? Justify your answer

188 11. Solve for x. 12. Solve for x. 13. Solve for x. 14. Solve for x. 9.2 Quiz 1 B: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Use the diagram to match the circle parts with the best description

189 1. FJ A. major arc 2. GE B. minor arc 3. GH C. radius 4. BC D. chord 5. BJ E. common internal tangent 6. DB F. common external tangent 7. BC G. diameter 8. ĜJH H. secant 9. Find the perimeter of the triangle circumscribed about the circle. 10. Is the segment a tangent? Justify your answer. 11. Solve for x. 12. Solve for x. 13. Solve for x

190 14. Solve for x. 9.3 Quiz 1 C: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs Use the diagram to match the circle parts with the best description. 1. FJ A. minor arc 2. GE B. major arc 3. GH C. chord 4. BC D. radius 5. BJ E. common external tangent 6. DB F. common internal tangent 7. BC G. secant 8. ĜJH H. diameter 9. Find the perimeter of the triangle circumscribed about the circle. 10. Is the segment a tangent? Justify your answer

191 11. Solve for x. 12. Solve for x. 13. Solve for x. 14. Solve for x. 9.4 Quiz 2 A: Sections 3 and 4: Properties of Chords and Inscribed Angles Find the value of x in the following diagrams

192

193 Quiz 2 B: Sections 3 and 4: Properties of Chords and Inscribed Angles Find the value of x in the following diagrams

194

195 Quiz 2 C: Sections 3 and 4: Properties of Chords and Inscribed Angles Find the value of x in the following diagrams

196

197 9.7 Quiz 3 A: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Find the value of x in the diagrams

198 Quiz 3 B: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Find the value of x in the diagrams

199

200 Quiz 3 C: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Find the value of x in the diagrams

201

202 Quiz 4: Extension: Equations of Circles 1. What two pieces of information are required to write an equation of a circle? 2. What is the equation of the circle with center (-3, 7) and radius 3? 3. What are the center and radius of the circle with equation (x 2) 2 + (y + 1) 2 = 81? center: radius: 4. What is the equation of the circle below? 194

203 5. Graph the circle with equation: (x + 4) 2 + (y 3) 2 = 49? 9.11 Free Response Test Use the diagram to identify the following parts of the circle. 1. chord 2. minor arc 3. secant 4. tangent 5. point of tangency 6. major arc 7. Find the perimeter of the triangle circumscribed about the circle. 8. Solve for x

204 9. Solve for x. Solve for x in the following diagrams

205

206 9.12 Multiple Choice Test 1. Which term best describes the diagram. (a) congruent (b) internally tangent (c) externally tangent (d) concentric 2. Which term best describes a line which intersects a circle in two points. (a) chord (b) tangent (c) diameter (d) secant 3. Circles with the same center are called. (a) concentric (b) congruent (c) internally tangent (d) common center 4. How many common tangents do the circles below have? (a) 1 (b) 2 (c) 3 (d) 4 5. Which statement is true about congruent circles. (a) radii are congruent (b) same center (c) chords are congruent (d) congruent inscribed angles Solve for x in the diagrams below

207 6. (a) 109 (b) 71 (c) 142 (d) (a) 18 (b) 17 (c) 19 (d) (a) 1 (b) 2 (c) 3 (d) 0 9. (a) 77 (b) 103 (c) 180 (d)

208 10. (a) 34 (b) 35 (c) 53 (d) (a) 155 (b) 75 (c) 25 (d) (a) 83 (b) 138 (c) 97 (d) (a) 85 (b) 95 (c) 90 (d)

209 (a) 174 (b) 194 (c) 196 (d) (a) 21 (b) 20 (c) 19 (d) (a) 15 (b) 10 (c) 12 (d) 14 (a) 24 (b) 20 (c) 18 (d) Answers for Chapter 9 Assessment Quiz 1 A: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs 1. G 201

210 2. F 3. H 4. D 5. A 6. C 7. B 8. E yes, the lengths form a right triangle proving that the segment is perpendicular to the radius and thus a tangent Quiz 1 B: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs 1. C 2. F 3. D 4. H 5. E 6. G 7. B 8. A yes, the lengths form a right triangle proving that the segment is perpendicular to the radius and thus a tangent Quiz 1 C: Sections 1 and 2: Parts of Circles, Tangent Lines and Properties of Arcs 1. D 2. E 3. C 4. G 5. F 6. H 7. A 8. B yes, the lengths form a right triangle proving that the segment is perpendicular to the radius and thus a tangent

211 Quiz 2 A: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 2 B: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 2 C: Sections 3 and 4: Properties of Chords and Inscribed Angles Quiz 3 A: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents 203

212 Quiz 3 B: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Quiz 3 C: Sections 5 and 6: Angles and Segments from Chords, Secants and Tangents Quiz 4: Extension: Equations of Circles 1. center and radius 2. (x + 3) 2 + (y 7) 2 = 9 3. center (2, -1); radius 9 4. (x 4) 2 + (y 5) 2 =

213 5. Free Response Test 1. GE 2. Answers vary, any two letter which are less than 180 apart on the circle. 3. HB 4. AC 5. A 6. Any three letters which mark off an arc greater than Multiple Choice Test 1. c 2. d 3. a 4. d 5. a 6. b 205

214 7. c 8. a 9. a 10. d 11. c 12. c 13. b 14. d 15. c 16. d 17. c 206

215 Chapter 10 Perimeter and Area Assessment:Chapter Quiz 1 A: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons Find the perimeter and area of the following polygons. For some figures you may need to use the Pythagorean Theorem to find unknown lengths. Round your answers to the nearest tenth Perimeter Area 3. Perimeter Area Perimeter 207

216 Area Perimeter Area 6. Perimeter Area 7. Perimeter Area Perimeter Area 8. Find the perimeter and area of a rectangle with dimensions 5 m by 9 m. 9. If the area of a square is 64 in 2, what is the perimeter? 10. The perimeter of an equilateral triangle is 24 cm. What is its area? 11. The ratio of lengths between two similar polygons is 2:3. The perimeter of the smaller polygon is 12 in. What is the perimeter of the larger polygon? If the area of the larger polygon is 27 in, what is the area of the smaller polygon? 12. The areas of two similar polygons are in the ratio 25:36. Find the length ratio between them

217 10.2 Quiz 1 B: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons Find the perimeter and area of the following polygons. For some figures you may need to use the Pythagorean Theorem to find unknown lengths. Round your answers to the nearest tenth Perimeter Area 3. Perimeter Area 4. Perimeter Area 5. Perimeter Area 209

218 6. Perimeter Area 7. Perimeter Area Perimeter Area 8. Find the perimeter and area of a rectangle with dimensions 4 m by 9 m. 9. If the area of a square is 49 in 2, what is the perimeter? 10. The perimeter of an equilateral triangle is 30 cm. What is its area? 11. The ratio of lengths between two similar polygons is 2:3. The perimeter of the smaller polygon is 14 in. What is the perimeter of the larger polygon? If the area of the larger polygon is 36 in, what is the area of the smaller polygon? 12. The areas of two similar polygons are in the ratio 49:36. Find the length ratio between them Quiz 1 C: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons Find the perimeter and area of the following polygons. For some figures you may need to use the Pythagorean Theorem to find unknown lengths. Round your answers to the nearest tenth. 1. Perimeter Area 210

219 2. 3. Perimeter Area 4. Perimeter Area 5. Perimeter Area 6. Perimeter Area Perimeter Area 211

220 7. Perimeter Area 8. Find the perimeter and area of a rectangle with dimensions 5 m by 11 m. 9. If the area of a square is 81 in 2, what is the perimeter? 10. The perimeter of an equilateral triangle is 36 cm. What is its area? 11. The ratio of lengths between two similar polygons is 2:3. The perimeter of the smaller polygon is 16 in. What is the perimeter of the larger polygon? If the area of the larger polygon is 54 in, what is the area of the smaller polygon? 12. The areas of two similar polygons are in the ratio 25:64. Find the length ratio between them Quiz 2 A: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Use the circles below to find the requested measures. Round your answers to the nearest tenth Circumference Area Circumference Area 212

221 3. 4. Circumference = 12π Radius Area 5. Length of PQ 6. Length of PQ 7. Radius Area 213

222 8. 9. Central Area Area 10. The diameter of a wheel on George s bicycle is 30 cm. How many revolutions will the wheel make is George rides his bike 2 km. Remember, 100 cm = 1 m and 1000 m = 1 km. 11. Bernard wants to pant 1 tulip bulb every 6 inches around his circular pool in his backyard. The diameter of the pool is 12 ft. How many tulip bulbs does he need? Give your answer to the nearest tulip bulb. 12. Mario s Pizza makes its pizza with pepperoni pieces in the outside crust. If they claim to put 1 piece per 1 inch of crust how many pieces of pepperoni are in their super large with diameter 20 inches? 10.5 Quiz 2 B: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Use the circles below to find the requested measures. Round your answers to the nearest tenth Circumference Area 214

223 3. Circumference Area 4. Circumference = 16π Radius Area 5. Length of PQ 6. Length of PQ 7. Radius Area 215

224 8. 9. Central Angle Area 10. The diameter of a wheel on George s bicycle is 25 cm. How many revolutions will the wheel make is George rides his bike 2 km. Remember, 100 cm = 1 m and 1000 m = 1 km. 11. Bernard wants to pant 1 tulip bulb every 8 inches around his circular pool in his backyard. The diameter of the pool is 13 ft. How many tulip bulbs does he need? Give your answer to the nearest tulip bulb. 12. Mario s Pizza makes its pizza with pepperoni pieces in the outside crust. If they claim to put 1 piece per 1 inch of crust how many pieces of pepperoni are in their super large with diameter 21 inches? 10.6 Quiz 2 C: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors Use the circles below to find the requested measures. Round your answers to the nearest tenth Circumference Area 216

225 3. Circumference Area 4. Circumference = 18π Radius Area 5. Length of PQ 6. Length of PQ 7. Radius Area 217

226 8. 9. Central Angle Area 10. The diameter of a wheel on George s bicycle is 35 cm. How many revolutions will the wheel make is George rides his bike 2 km. Remember, 100 cm = 1 m and 1000 m = 1 km. 11. Bernard wants to pant 1 tulip bulb every 10 inches around his circular pool in his backyard. The diameter of the pool is 15 ft. How many tulip bulbs does he need? Give your answer to the nearest tulip bulb. 12. Mario s Pizza makes its pizza with pepperoni pieces in the outside crust. If they claim to put 1 piece per 1 inch of crust how many pieces of pepperoni are in their super large with diameter 22 inches? 10.7 Free Response Test Match the formula with the figure. 1. Rectangle or Parallelogram A. A = π r 2 2. Square B. A = 1 2 bh 3. Triangle C. A = bh 4. Kite or Rhombus D. A = 1 2 d 1d 2 5. Trapezoid E. A = s 2 6. Circle F. A = 1 2 (b 1 + b 2 )h Find the perimeter and area of the following figures. 7. Perimeter Area 218

227 8. 9. Perimeter Area 10. Perimeter Area 11. Perimeter Area 12. Perimeter Area Perimeter Area 219

228 Length of PQ 15. Radius 16. Length of PQ 17. Area 18. Area 220

229 Radius 19. What is the diameter of a circle with circumference 45π? 20. A sector of a circle with diameter 20 ft has area 20π f t. What is the measure of the central angle of this sector? 10.8 Multiple Choice Test Fill in the blanks. 1. The base and height of a figure must always be. (a) parallel (b) congruent (c) similar (d) perpendicular 2. The formula 2πr gives the of a circle. (a) circumference (b) diameter (c) area (d) arc length 3. The area of a sector is a fraction of the circle s area based on the ratio. central angle 180 central angle 360 (a) (b) (c) radius 180 (d) radius Find the perimeter and area of a rectangle with dimensions 9 ft by 12 ft. (a) P = 40 f t, A = 108 f t 2 (b) P = 42 f t, A = 36 f t 2 (c) P = 21 f t, A = 54 f t 2 (d) P = 42 f t, A = 108 f t 2 5. The length of a diagonal of a rectangle is 25 m and the rectangle s width is 7 m. Find the area of the rectangle. (a) 175 m 2 (b) 150 m 2 (c) 168 m 2 (d) 600 m 2 6. The length of the altitude in an equilateral triangle is 7 3 yd. Find the perimeter of the triangle. (a) 21 3 yd (b) 21 yd (c) 42 3 yd (d) 42 yd 7. The diagonals of a rhombus are 25 cm and 14 cm. What is the area of the rhombus? (a) 350 cm 2 (b) 78 cm 2 (c) 175 cm 2 (d) 156 cm

230 8. The area of a trapezoid is 63 in 2. If the lengths of the bases are 5 in and 16 in, what is the height of the trapezoid? (a) 3 in (b) 6 in (c) 9 in (d) 12 in 9. The ratio of the areas of two similar polygons is 1:16. What is the ratio of their perimeters? (a) 1:16 (b) 1:8 (c) 1:4 (d) 1: The ratio of the lengths of two similar polygons is 5:7. Given that the area of the smaller polygon is 75 m 2, find the area of the larger polygon. (a) 147 m 2 (b) 105 m 2 (c) 210 m 2 (d) 294 m What is the area of a circle with radius 3 in? (a) 3π in 2 (b) 6π in 2 (c) 9π in 2 (d) 12π in What is the area of a sector of a circle with radius 8 cm if the central angle measure is 135. (a) 12π cm 2 (b) 18π cm 2 (c) 22π cm 2 (d) 24π cm If the length of an arc in a circle with diameter 24 m is 8π m, what is the measure of the central angle that intercepts the arc? (a) 60 (b) 90 (c) 120 (d) If the area of a sector of a circle with central angle 210 is 84π m 2, what is the length of the radius? (a) 6 m (b) 12 m (c) 24 m (d) 18 m 15. If the wheel of a bicycle with diameter 15 in makes 500 revolutions, how far has the bicycle travelled? (a) 33.3 in (b) 7500 in (c) 23,561.9 in (d) in 222

231 10.9 Answers for Chapter 10 Assessment Quiz 1 A: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons 1. P = 66, A = P = 28, A = P = 19.7, A = P = 20, A = P = 17.2, A = P = 48, A = P = 45.4, A = P = 28 m, A = 45 m in cm P = 18 in, 12 in :6 Quiz 1 B: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons 1. P = 66, A = P = 32, A = P = 24.8, A = P = 40, A = P = 37.7, A = P = 52, A = P = 37.5, A = P = 26 m, A = 36 m in cm P = 21 in, 16 in :6 Quiz 1 C: Sections 1, 2 and 3: Triangles, Parallelograms, Trapezoids, Rhombi, Kites and Areas of Similar Polygons 1. P = 66, A = P = 28, A = P = 19.7, A = P = 20, A = P = 17.2, A = P = 48, A = P = 45.4, A = P = 28 m, A = 45 m in cm P = 24 in, 12 in :

232 Quiz 2 A: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors 1. C = 50.3; A = C = 44.0; A = r = 6; A = revolutions bulbs pieces Quiz 2 B: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors 1. C = 47.1; A = C = 50.3; A = r = 8; A = revolutions bulbs pieces Quiz 2 C: Sections 4 and 5: Circumference and Arc Length and Area of Circles and Sectors 1. C = 53.4; A = C = 62.8; A = r = 9; A = revolutions bulbs pieces Free Response Test 1. C 2. E 224

233 3. B 4. D 5. F 6. A 7. P = 56; A = P = 38; A = P = 38; A = P = 33.4; A = P = 68; A = P = 120; A = Multiple Choice Test 1. d 2. a 3. b 4. c 5. c 6. d 7. c 8. b 9. c 10. a 11. c 12. d 13. c 14. b 15. c 225

234 Chapter 11 Surface Area and Volume Assessment:Chapter Quiz 1 A: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Match the figures with their names. 1. Regular Octahedron 2. Rectangular Prism 3. Pentagonal Prism 4. Square Pyramid 5. Regular Dodecahedron Use the figures above to fill in the blanks below. 6. Figure B has edges, faces and vertices. 7. Figure D has edges, faces and vertices. Find the surface area of the figures below

235 The base is a square

236 11.2 Quiz 1 B: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Match the figures with their names. 1. Regular Dodecahedron 2. Pentagonal Prism 3. Square Pyramid 4. Rectangular Prism 5. Regular Octahedron Use the figures above to fill in the blanks below. 6. Figure C has edges, faces and vertices. 7. Figure B has edges, faces and vertices. Find the surface area of the figures below The base is a square

237 Quiz 1 C: Sections 1, 2 and 3: Exploring Solids and Surface Area of Prisms, Cylinders, Pyramids and Cones Match the figures with their names. 1. Rectangular Prism 2. Regular Dodecahedron 3. Square Pyramid 4. Regular Octahedron 5. Pentagonal Prism Use the figures above to fill in the blanks below. 6. Figure E has edges, faces and vertices. 7. Figure C has edges, faces and vertices. Find the surface area of the figures below

238 The base is a square Quiz 2 A: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Find the volume of the following solids

239 Find the surface area and volume of the following solids

240 9. Find the surface area and volume of the following solids Quiz 2 B: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Find the volume of the following solids

241 Find the surface area and volume of the following solids Find the surface area and volume of the following solids

242 Quiz 2 C: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres Find the volume of the following solids

243 5. 6. Find the surface area and volume of the following solids Find the surface area and volume of the following solids

244 Quiz 4: Extension: Similar Solids 1. Determine whether the two regular hexagonal pyramids are similar. Explain your conclusion. 2. The following cylinders have surface areas in the ratio 9:25. (a) What is the ratio of their lengths or scale factor between them? (b) Find the height of the smaller cylinder. (c) What is the ratio of their volumes? (d) Find the volume of the larger cylinder. 3. The ratio of volumes between two similar figures is 1:216. (a) What is the ratio of their lengths? (b) What is the ratio of their surface areas? (c) If the surface area of the larger figure is 252 u 2, what is the surface area of the smaller figure? 4. Two spheres have radii 3 and 7. (a) What is the ratio of their surface areas? (b) What is the ratio of their volumes? 5. Two similar figures have surface areas 75 u 2 and 243 u 2. Find the volume of the smaller figure if the larger one has volume 3645 u

245 11.8 Free Response Test Recall that Euler s Theorem states that in a polyhedron F + V = E + 2. Use this information for questions 1 and In a five faced polygon there are eight edges. How many vertices does it have? 2. A three dimensional figure has 8 faces, 12 edges and 8 vertices. Is it a polyhedron? Sketch the nets for the following solids Find the surface area and volume of the following figures

246 A hemisphere has total surface area of 147π u 2. What is its radius? 13. A right cone has diameter 18 cm and height 40 cm, what is its slant height? 14. A square pyramid with height 12 m has volume 100 m 3. What is the length of each side of the base? 15. An ice cream cone is filled with ice cream and the scoop on top is a perfect hemisphere with radius 1.5 in. If the cone has diameter 2 in and height 3 in, what is the volume of the ice cream? 11.9 Multiple Choice Test 1. According to Euler s Formula, the number of faces, edges and vertices must follow the rule: (a) F + V = E + 2 (b) F + E = V + 2 (c) V + E = F + 2 (d) E + F = V 2 2. Which of the following regular polygons cannot be used to create a regular polyhedron? (a) square (b) triangle (c) pentagon (d) hexagon 3. Which of the following is not a polyhedron? 238

247 (a) (b) (c) (d) 4. Which of the following is not a net for a cube. (a) (b) (c) (d) 5. What are the required dimensions of a label for a soup can with height 8 in and diameter 6 in? (a) 8 in by 6 in (b) 6π in by 8 in (c) 6 in by 8π in 239

248 (d) 3π in by 8 in 6. Charlie takes a 3 ft by 3 ft square piece of cardboard and cuts out 6 in squares from the corners as shown in the diagram below. If Charlie folds up the sides along the dashed lines, what is the volume of the open topped box? (a) 54 f t 2 (b) 37.5 f t 2 (c) 24 f t 2 (d) 288 f t 2 Solve the following problems. You may find it helpful to sketch the figure. 7. A trapezoidal prism has base area of 25 cm 2. What is the volume of the trapezoidal prism if the height is 12 cm? (a) 600 cm 3 (b) 450 cm 3 (c) 150 cm 3 (d) 300 cm 3 8. The surface area of a cube is 150 in 2. What is the volume of the cube? (a) 125 in 3 (b) 250 in 3 (c) 200 in 3 (d) 175 in 3 9. The volume of a sphere is 288π m 3. What is the surface area of the sphere? (a) 24π (b) 144π (c) 288π (d) 244π 10. The volume of a square pyramid is 48 cm 2. If the area of the base is 16 cm 2, what is the height of the pyramid? (a) 3 cm (b) 6 cm (c) 9 cm (d) 12 cm 11. The surface area of a cone is 90π. If the radius is 5, what is the slant height? (a) 10 (b) 11 (c) 12 (d)

249 12. The volume of a trapezoidal prism is 231 f t 3. If the area of a base is 21 f t 2, what is the height of the prism? (a) 11 ft (b) 12 ft (c) 13 ft (d) 14 ft 13. The surface area of a cylinder with radius 5 in is 120π in 2. What is the height of the cylinder? (a) 5 in (b) 6 in (c) 7 in (d) 8 in 14. The radius and height of a cone are 9 m and 12 m respectively. What is the slant height of the cone? (a) 12 m (b) 13 m (c) 14 m (d) 15 m 15. The surface area of a square pyramid is 144 f t 2. If the length of a side of the base is 6 ft, what is the slant height? (a) 6 ft (b) 9 ft (c) 12 ft (d) 15 ft Answers for Chapter 11 Assessment Quiz 1 A: Sections 1, 2 and 3: Pyramids and Cones Exploring Solids and Surface Area of Prisms, Cylinders, 1. C 2. E 3. B 4. D 5. A 6. 15; 7; ; 5; Quiz 1 B: Sections 1, 2 and 3: Pyramids and Cones Exploring Solids and Surface Area of Prisms, Cylinders, 1. A 241

250 2. B 3. D 4. E 5. C 6. 12; 8; ; 7; Quiz 1 C: Sections 1, 2 and 3: Pyramids and Cones Exploring Solids and Surface Area of Prisms, Cylinders, 1. E 2. A 3. D 4. C 5. B 6. 12; 6; ; 8; Quiz 2 A: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres S.A ; V S.A ; V S.A ; V S.A. = 818; V = S.A ; V Quiz 2 B: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres

251 S.A ; V S.A ; V S.A ; V S.A. = 658; V = S.A ; V Quiz 2 C: Sections 4 and 5: Volume of Prisms, Cylinders, Pyramids and Cones, Surface Area and Volume of Spheres S.A ; V S.A ; V S.A ; V S.A. = 938; V = S.A ; V Quiz 4: Extension: Similar Solids 1. yes, the lengths are in the same ratio, 3:5 2. (a) 3:5 (b) 27 (c) 27:125 (d) 12500π 3. (a) 1:6 (b) 1:36 (c) 7 u 2 4. (a) 9:49 (b) 27: u 3 Free Response Test No,

252 S.A. = 176; V = S.A ; V S.A. = 800; V = S.A ; V S.A ; V S.A. = 693.6; V = u cm m in 3 Multiple Choice Test 1. a 2. d 3. d 4. c 5. b 6. c 7. d 8. a 9. b 10. c 11. d 12. a 13. c 14. d 15. b 244