2013 CPB Geometry Final Study Guide Multiple Choice: Identify the choice that best completes the statement or answers the question.

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1 2013 CPB Geometry Final Study Guide Multiple Choice: Identify the choice that best completes the statement or answers the question. 1. Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois. a. Sara Lucas lives in Springfield. b. Jonah Lincoln lives in Springfield, Illinois. c. Billy Jones lives in Chicago, Illinois. d. Erin Naismith lives in Springfield, Massachusetts. 2. What must be true about the slopes of two perpendicular lines, neither of which is vertical? a. The slopes are equal. b. The slopes have product 1. c. The slopes have product 1. d. One of the slopes must be Which statement is the Law of Syllogism? a. If is a true statement and p is true, then q is true. b. If is a true statement and q is true, then p is true. c. If and are true statements, then is a true statement. d. If and are true statements, then is a true statement. 4. Which angle is a right angle? a. c. b. d. 5. What is the graph of y = 3 5 x + 3? a. c. y y x x b. d y y x x 2 4 6

2 6. Which pair of triangles is congruent by ASA? a. c. b. d. 7. Write an equation in slope-intercept form of the line through point P(2, 8) with slope 5. a. y 8 = 5(x 2) c. y = 5x 2 b. y 2 = 5(x 8) d. y = 5x Sarah has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Sarah the garden with greatest area? The diagrams are not to scale. a. c. 16 ft 17 ft 15 ft 14 ft b. 18 ft d. 19 ft 13 ft 12 ft

3 9. In the figure shown,. Which of the following statements is false? Not drawn to scale a. b. AEB and BEC are adjacent angles. c. d. DEC and AEB are adjacent angles. 10. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is. a. b. c. d. 11. Which statement is true? a. All rectangles are parallelograms. b. All parallelograms are rectangles. c. All quadrilaterals are rectangles. d. All quadrilaterals are squares. 12. Classify the figure in as many ways as possible. a. rectangle, square, quadrilateral, parallelogram, rhombus b. rectangle, square, parallelogram c. rhombus, quadrilateral, square d. square, rectangle, quadrilateral

4 13. Which statement is not necessarily true? Given: is the bisector of D J K L E a. K is the midpoint of. c. b. DJ = DL d. DJ = JE 14. Which Venn diagram is NOT correct? a. c. Rhombuses Quadrilaterals Squares Kites b. d. Squares Parallelograms Rectangles Rhombuses 15. How are the two angles related? Drawing not to scale a. supplementary c. complementary b. vertical d. adjacent

5 16. Judging by appearances, which figure is a trapezoid? a. c. b. d. Short Answer 17. If, find the value of FG. The drawing is not to scale. E F G 18. Name an angle supplementary to 19. Name the ray in the figure. P Q 20. What plane contains points B, C, and D?

6 21. What are the names of three collinear points? P M F C D N 22. What segment is congruent to? A B C D E Find the area of the circle in terms of. 10 in. 24. What is the length of? A B C D Which point is the midpoint of? A B C D E If and, then what is the measure of The diagram is not to scale.

7 Number of Customers 27. Bob s Internet Services designs web sites and recently began a weekly advertising campaign. Bob noticed an increase in his customers over a period of five consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers Bob will have in the seventh week. 10 y x Week 28. Identify the hypothesis and conclusion of this conditional statement: If today is Wednesday, then tomorrow is Thursday. 29. Based on the pattern, what are the next two terms of the sequence? 7, 13, 19, 25,... Use the diagram to find the following. h a b Identify a pair of alternate exterior angles. 31. What are three pairs of corresponding angles? 32. Find Drawing not to scale

8 33. What is the relationship between and? m n 34. Name the Property of Congruence that justifies the statement: If. 35. Find The diagram is not to scale. G H p 42 r 36. Name the Property of Congruence that justifies this statement: If. 37. What is the value of x? (6x 7) (5x + 10) Drawing not to scale

9 38. The two triangles are congruent as suggested by their appearance. Find the value of g. The diagrams are not to scale. g 37 b 25 d 24 f 7 e 53 c 39. What is the equation in point-slope form for the line parallel to y = 7x + 1 that contains P( 3, 5)? 40. Find the value of x. 20 3x If BCDE is congruent to OPQR, then is congruent to 42. What is the slope of the line shown? 10 8 ( 4, 6) 4 2 y x 2 4 (9, 5)

10 43. What are two other names for? E H F 2 3 G 44. What is the value of x? xº Drawing not to scale 45. Find the sum of the measures of the angles of the figure. 46. Find the values of the variables in the parallelogram. The diagram is not to scale z y x

11 47. Write the conditional statement that the Venn diagram illustrates. Quadrilaterals Squares 48. Solve for x. Justify each step.

12 Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: Recognize conditional statements and their parts NAT: G.5.a STA: G.G.2 TOP: 2-2 Problem 3 Finding the Truth Value of a Conditional KEY: conditional statement counterexample 2. ANS: C PTS: 1 DIF: L2 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines NAT: G.3.g G.4.a G.4.d STA: G.G.11 G.G.12 G.G.13 TOP: 3-8 Problem 3 Checking for Perpendicular Lines KEY: slopes of perpendicular lines perpendicular lines reasoning 3. ANS: C PTS: 1 DIF: L2 REF: 2-4 Deductive Reasoning OBJ: Use the Law of Detachment and the Law of Syllogism STA: G.G.2 TOP: 2-4 Problem 2 Using the Law of Syllogism KEY: deductive reasoning Law of Syllogism 4. ANS: D PTS: 1 DIF: L2 REF: 1-4 Measuring Angles OBJ: Find and compare the measures of angles NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-4 Problem 2 Measuring and Classifying Angles KEY: obtuse angle straight angle right angle acute angle 5. ANS: A PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations NAT: G.3.g G.4.a G.4.d STA: G.G.11 G.G.12 TOP: 3-7 Problem 2 Graphing Lines KEY: slope-intercept form graphing 6. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Prove two triangles congruent using the ASA Postulate and the AAS Theorem NAT: G.2.e G.3.e G.5.e STA: G.G.2 G.G.4 TOP: 4-3 Problem 1 Using ASA KEY: ASA 7. ANS: C PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations NAT: G.3.g G.4.a G.4.d STA: G.G.11 G.G.12 TOP: 3-7 Problem 3 Writing Equations of Lines KEY: slope-intercept form 8. ANS: A PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes NAT: M.1.c M.1.f M.2.a G.3.b A.4.e STA: G.G.3 G.M.1 TOP: 1-8 Problem 4 Finding Area of a Rectangle KEY: rectangle area word problem problem solving 9. ANS: D PTS: 1 DIF: L4 REF: 1-5 Exploring Angle Pairs OBJ: Identify special angle pairs and use their relationships to find angle measures NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: adjacent angles supplementary angles vertical angles 10. ANS: D PTS: 1 DIF: L3 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon NAT: M.1.d G.3.f STA: G.G.1 G.G.7

13 TOP: 6-1 Problem 1 Finding a Polygon Angle Sum KEY: Polygon Angle-Sum Theorem 11. ANS: A PTS: 1 DIF: L2 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Define and classify special types of parallelograms NAT: G.1.c G.3.f STA: G.G.1 TOP: 6-4 Problem 1 Classifying Special Parallelograms KEY: reasoning parallelogram quadrilateral rectangle rhombus special quadrilaterals 12. ANS: A PTS: 1 DIF: L2 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Define and classify special types of parallelograms NAT: G.1.c G.3.f STA: G.G.1 TOP: 6-4 Problem 1 Classifying Special Parallelograms KEY: special quadrilaterals quadrilateral parallelogram rhombus square rectangle 13. ANS: D PTS: 1 DIF: L3 REF: 5-2 Perpendicular and Angle Bisectors OBJ: Use properties of perpendicular bisectors and angle bisectors NAT: G.3.c TOP: 5-2 Problem 1 Using the Perpendicular Bisector Theorem KEY: Perpendicular Bisector Theorem perpendicular bisector reasoning 14. ANS: B PTS: 1 DIF: L2 REF: 6-4 Properties of Rhombuses, Rectangles, and Squares OBJ: Define and classify special types of parallelograms NAT: G.1.c G.3.f STA: G.G.1 TOP: 6-4 Problem 1 Classifying Special Parallelograms KEY: reasoning quadrilateral Venn Diagram NOT: TC 12, MC, Static. 15. ANS: A PTS: 1 DIF: L2 REF: 1-5 Exploring Angle Pairs OBJ: Identify special angle pairs and use their relationships to find angle measures NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: supplementary angles 16. ANS: A PTS: 1 DIF: L2 REF: 6-6 Trapezoids and Kites OBJ: Verify and use properties of trapezoids and kites NAT: G.1.c G.3.f STA: G.G.1 TOP: 6-6 Problem 1 Finding Angle Measures in Trapezoids KEY: trapezoid SHORT ANSWER 17. ANS: 18 PTS: 1 DIF: L2 REF: 1-3 Measuring Segments OBJ: Find and compare lengths of segments NAT: G.3.b TOP: 1-3 Problem 2 Using the Segment Addition Postulate KEY: segment segment length 18. ANS: PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: Identify special angle pairs and use their relationships to find angle measures NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: supplementary angles

14 19. ANS: PTS: 1 DIF: L2 REF: 1-2 Points, Lines, and Planes OBJ: Understand basic terms and postulates of geometry NAT: G.3.b G.4.b TOP: 1-2 Problem 2 Naming Segments and Rays KEY: ray 20. ANS: The plane on the top of the figure. PTS: 1 DIF: L2 REF: 1-2 Points, Lines, and Planes OBJ: Understand basic terms and postulates of geometry NAT: G.3.b G.4.b TOP: 1-2 Problem 4 Using Postulate 1-4 KEY: plane point 21. ANS: Points F, C, and D are collinear. PTS: 1 DIF: L3 REF: 1-2 Points, Lines, and Planes OBJ: Understand basic terms and postulates of geometry NAT: G.3.b G.4.b TOP: 1-2 Problem 1 Naming Points, Lines, and Planes KEY: collinear point 22. ANS: PTS: 1 DIF: L3 REF: 1-3 Measuring Segments OBJ: Find and compare lengths of segments NAT: G.3.b TOP: 1-3 Problem 3 Comparing Segment Lengths KEY: segment length segment 23. ANS: 25 in. 2 PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: Find the perimeter or circumference of basic shapes NAT: M.1.c M.1.f M.2.a G.3.b A.4.e STA: G.G.3 G.M.1 TOP: 1-8 Problem 5 Finding Area of a Circle KEY: area circle 24. ANS: 14 PTS: 1 DIF: L2 REF: 1-3 Measuring Segments OBJ: Find and compare lengths of segments NAT: G.3.b TOP: 1-3 Problem 1 Measuring Segment Lengths KEY: segment segment length 25. ANS: D PTS: 1 DIF: L2 REF: 1-3 Measuring Segments OBJ: Find and compare lengths of segments NAT: G.3.b TOP: 1-3 Problem 4 Using the Midpoint KEY: segment length segment midpoint

15 26. ANS: 61 PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: Find and compare the measures of angles NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-4 Problem 4 Using the Angle Addition Postulate KEY: Angle Addition Postulate 27. ANS: Laisha will have 13 customers. PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive Reasoning OBJ: Use inductive reasoning to make conjectures NAT: G.5.a STA: G.G.2 TOP: 2-1 Problem 4 Making a Prediction KEY: conjecture inductive reasoning pattern word problem problem solving 28. ANS: Hypothesis: Today is Wednesday. Conclusion: Tomorrow is Thursday. PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: Recognize conditional statements and their parts NAT: G.5.a STA: G.G.2 TOP: 2-2 Problem 1 Identifying the Hypothesis and the Conclusion KEY: conditional statement hypothesis conclusion 29. ANS: 31, 37 PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive Reasoning OBJ: Use inductive reasoning to make conjectures NAT: G.5.a STA: G.G.2 TOP: 2-1 Problem 1 Finding and Using a Pattern KEY: pattern inductive reasoning 30. ANS: PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: Identify angles formed by two lines and a transversal NAT: M.1.d G.3.g STA: G.G.6 TOP: 3-1 Problem 2 Identifying an Angle Pair KEY: transversal angle pair 31. ANS: angles 2 & 4, 3 & 5, and 1 & 7 PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: Identify angles formed by two lines and a transversal NAT: M.1.d G.3.g STA: G.G.6 TOP: 3-1 Problem 2 Identifying an Angle Pair KEY: angle pair transversal 32. ANS: 55 PTS: 1 DIF: L2 REF: 2-6 Proving Angles Congruent OBJ: Prove and apply theorems about angles NAT: G.5.b STA: G.G.2 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem

16 KEY: Vertical Angles Theorem vertical angles 33. ANS: alternate interior angles PTS: 1 DIF: L3 REF: 3-1 Lines and Angles OBJ: Identify angles formed by two lines and a transversal NAT: M.1.d G.3.g STA: G.G.6 TOP: 3-1 Problem 3 Classifying an Angle Pair KEY: angle pair transversal 34. ANS: Symmetric Property PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry OBJ: Connect reasoning in algebra and geometry NAT: G.5.b STA: G.G.2 TOP: 2-5 Problem 2 Using Properties of Equality and Congruence KEY: Properties of Congruence 35. ANS: 42º PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines OBJ: Use properties of parallel lines to find angle measures NAT: M.1.d G.3.g STA: G.G.6 TOP: 3-2 Problem 3 Finding Measures of Angles KEY: angle parallel lines transversal 36. ANS: Transitive Property PTS: 1 DIF: L2 REF: 2-5 Reasoning in Algebra and Geometry OBJ: Connect reasoning in algebra and geometry NAT: G.5.b STA: G.G.2 TOP: 2-5 Problem 2 Using Properties of Equality and Congruence KEY: Properties of Congruence 37. ANS: 17 PTS: 1 DIF: L3 REF: 2-6 Proving Angles Congruent OBJ: Prove and apply theorems about angles NAT: G.5.b STA: G.G.2 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles Vertical Angles Theorem 38. ANS: 25 PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts NAT: G.2.e G.3.e TOP: 4-1 Problem 2 Using Congruent Parts KEY: congruent figures corresponding parts 39. ANS: y 5 = 7(x + 3) PTS: 1 DIF: L3 REF: 3-8 Slopes of Parallel and Perpendicular Lines OBJ: Relate slope to parallel and perpendicular lines NAT: G.3.g G.4.a G.4.d STA: G.G.11 G.G.12 G.G.13 TOP: 3-8 Problem 2 Writing Equations of Parallel Lines KEY: slopes of parallel lines parallel lines

17 40. ANS: 4 PTS: 1 DIF: L3 REF: 5-1 Midsegments of Triangles OBJ: Use properties of midsegments to solve problems NAT: G.3.c TOP: 5-1 Problem 2 Finding Lengths KEY: midpoint midsegment Triangle Midsegment Theorem 41. ANS: PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Recognize congruent figures and their corresponding parts NAT: G.2.e G.3.e TOP: 4-1 Problem 1 Finding Congruent Parts KEY: congruent figures corresponding parts word problem 42. ANS: PTS: 1 DIF: L3 REF: 3-7 Equations of Lines in the Coordinate Plane OBJ: Graph and write linear equations NAT: G.3.g G.4.a G.4.d STA: G.G.11 G.G.12 TOP: 3-7 Problem 1 Finding Slopes of Lines KEY: slope linear graph graph of line 43. ANS: and PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: Find and compare the measures of angles NAT: M.1.d G.3.b STA: G.G.6 TOP: 1-4 Problem 1 Naming Angles KEY: angle 44. ANS: 74 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: Use and apply properties of isosceles and equilateral triangles NAT: G.1.c G.2.e G.3.e STA: G.G.1 G.G.4 G.G.8 TOP: 4-5 Problem 2 Using Algebra KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 45. ANS: 720 PTS: 1 DIF: L2 REF: 6-1 The Polygon Angle-Sum Theorems OBJ: Find the sum of the measures of the interior angles of a polygon NAT: M.1.d G.3.f STA: G.G.1 G.G.7 TOP: 6-1 Problem 1 Finding a Polygon Angle Sum KEY: sum of angles of a polygon 46. ANS: PTS: 1 DIF: L4 REF: 6-2 Properties of Parallelograms

18 OBJ: Use relationships among sides and angles of parallelograms NAT: G.1.c G.3.f STA: G.G.1 TOP: 6-2 Problem 1 Using Consecutive Angles KEY: parallelogram opposite angles consecutive angles transversal 47. ANS: If a figure is a square, then it is a quadrilateral. PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: Recognize conditional statements and their parts NAT: G.5.a STA: G.G.2 TOP: 2-2 Problem 2 Writing a Conditional KEY: Venn Diagram conditional statement 48. ANS: Given Addition Property of Equality Simplify x = 14 Division Property of Equality Simplify PTS: 1 DIF: L4 REF: 2-5 Reasoning in Algebra and Geometry OBJ: Connect reasoning in algebra and geometry NAT: G.5.b STA: G.G.2 TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation KEY: Properties of Equality proof deductive reasoning DOK: DOK 3