FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1. Angle. Angle Addition Postulate. Angle Bisector. Length of a segment

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1 Name FALL SEMESTER EXAM Directions: You must show work for all the problems. Unit 1 Period Angle Angle Addition Postulate Angle Bisector Length of a segment Line Midpoint Right Angle Segment Segment Addition Postulate Segment Bisector True/False. If a statement is false, rewrite it so that it is true. 1. Coplanar lines are collinear. 2. A plane is determined by any 3 points. 3. A segment has one endpoint. 4. Supplementary angles have a sum of 90 o 5. A midpoint is any point equidistant from the endpoints of a segment. Find each length. 6. AB 7. BC 8. Find MP. 9. Describe the difference between the following notations: AB and AB 10. E is the midpoint of DF, DE 2x 4, and EF 3x 1. Find DE, DF, and EF. (DRAW A PICTURE!) 11. Q bisects PR, PQ 3y, and PR 42. Find y and QR. (DRAW A PICTURE!)

2 2 12. Name two lines that contain B. 13. Name two pairs of vertical angles. E A B C D Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent and and and and 3 ABD and BDE are supplementary. Find the measures of both angles. 18. m ABD (3x 12), m BDE (7x 32) 19. m ABD (12 x 12), m BDE (3x 48) ABD and BDC are complementary. Find the measures of both angles. 20. m ABD (5y 1), m BDC (3y 7) 21. m ABD (4y 5), m BDC (4y 8) BD bisects ABC. Find each of the following. (DRAW A PICTURE!) 22. m ABD if m ABD (6x 4) and m DBC (8x 4) 23. m ABC if m ABD (5y 3) and m DBC (3y 15) Unit 2 Complementary Angles Distance Formula Linear Pair Linear Pair Theorem Midpoint Formula Right Angle Congruence Theorem Supplementary Angles Vertical Angle Theorem Vertical Angles

3 Find the coordinates of the midpoint of each segment AB with endpoints A(4, 6) and B( 4,2) 2. CD with endpoints C(0, 8) and D (3,0) Use the distance formula to find the length of each segment with the given endpoints to the nearest tenth. 3. U (0,1) and V( 3, 9) 4. M(10, 1) and N(2, 5) 5. A figure has vertices at J( 2,3), K (0,3), L (0,1), and M ( 2,1). After a transformation, the image of the figure has vertices at J '(2,1), K '(4,1), L'(4, 1), and M '(2, 1). Draw the preimage and image. Then identify the transformation. Type of Transformation: 6. The coordinates of the vertices of DEF are D (2,3), E (1,1), and F (4,0). Find the coordinates for the image of DEF after the translation ( x, y) ( x 3, y 2). Draw the pre-image and image. D '(, ) E '(, ) F '(, ) 7. Find the coordinates for the image of RST with vertices R (1,4), S( 1, 1), and T( 5,1) after the translation ( x, y) ( x 2, y 4). R '(, ) S '(, ) T '(, ) Given the points F (3,5), G( 1,4), and H (5,0), draw FGH and its reflection across each of the following lines. 8. Reflection across the x axis 9. Reflection across the y axis

4 Unit 3 4 Addition Property of Equality Bi-conditional Statement Conditional Statement Converse Statement Counterexample Division Property of Equality Hypothesis Inductive Reasoning Inverse Statement Multiplication Property of Equality Reflexive Property of Equality Subtraction Property of Equality Find the next item in each pattern , 64, 53, , 6, 9, 12, -15,,,, Write the conditional statement from the given Venn Diagrams. a. b. Spiders Birds Tarantulas Blue Jays Using the given statement, tell what the hypothesis and conclusion are, and write the converse, inverse, and contrapositive for each conditional statement. 5. If a person is 16 years old, then the person can drive a car. Hypothesis: Conclusion: Converse: Inverse: Contrapositive:

5 5 6. Four angles are formed if two lines intersect. Hypothesis: Conditional: Converse: Inverse: Contrapositive: 7. Find a counterexample to each of the following statements: a. If a figure has 4 sides, then it is a rectangle. b. If an animal has 4 legs, then is is a dog. Write a justification for each step AB BC 5y 6 2y 21 3y y 15 y 5 PQ QR PR 3n 25 9n n n 5 n Solve each equation. Write a justification for each step. z 10. 5x 3 4( x 2) Write a justification for each step, given that m A 60 and m B 2m A. Statements Justification a. m A 60, m B 2m A b. m B 2(60 ) c. m B 120 d. m B m A 120 m A e. m A m B f. m A m B 180 g. A and B are supplementary.

6 Unit 4 6 Alternate Exterior Angles Alternate Exterior Angles Theorem Alternate Interior Angles Alternate Interior Angles Theorem Corresponding Angles Corresponding Angles Postulate Parallel Lines Parallel Lines Theorem Perpendicular lines or segments Perpendicular Lines Theorem Same Side Interior Angles Same-Side Interior Angles Theorem Transversal List all of the pairs of each of the following types of angles. 1. Alternate Interior Angles 2. Alternate Exterior Angles 3. Corresponding Angles 4. Same Side Interior Angles 5. Linear Pair of Angles 6. Vertical Angles > >

7 Find each angle measure m KLM 8. m PQR 9. m STU 10. m EFG 11. m CBY 12. Solve for x. 13. Find all missing angle measures: m 1 m 2 m 3 m 4 m 5 m 6 m o m 8 Unit 5 Equation of line in Point-Slope Form Equation of line in Slope-Intercept Form Slope Slope Formula Use slopes to determine whether the lines are parallel, perpendicular, or neither. 1. AB and CD for A(2, 1), B (7,2), C(2, 3), and D( 3, 6) 2. XY and ZW for X ( 2,5), Y(6, 2), Z( 3,6), and W (4,0)

8 8 Determine whether the lines are parallel, perpendicular, or coincide y x 4 and 2y 5x 4 4. x 2y 6 and 2 1 y x x 3y 15 and 3x 2y 16 2 What is the slope of the given line? 6. 3x 2y x 6y 13 Unit 6 Acute Triangle Base Angles of an Isosceles Triangle Base of an Isosceles Triangle Equiangular Triangle Corollary Equilateral Triangle Exterior Angle Exterior Angle Theorem Isosceles Triangle Isosceles Triangle Theorem Obtuse Triangle Remote Interior Angles Right Triangle Scalene Triangle Third Angles Theorem Triangle Sum Theorem Vertex Angle of an Isosceles Triangle

9 Classify the triangles by the sides and by the angles. 9 Sides Angles Find each angle measure. 5. m M 6. m XYZ 7. m C 8. m S 9. m N Given FGH JKL. Find each value. 10. KL 11. x

10 12. MNP RST. What are the values of x and y? 10 x = y = Solve for x. 13. A C 14. 2x + 3 4x 1 A 42 2x 14 B 2x 1 C B Unit 7 AAS Congruence Theorem ASA Congruence Postulate Congruent Angles Congruent Segments Congruent Triangles Corresponding Sides HL Congruence Theorem SAS Congruence Postulate SSS Congruence Postulate Determine whether the pairs of triangles are congruent or not. If they are, state which theorem or postulate proves their congruence VS bisects RST and RVT

11 What additional information is needed to prove the triangles congruent by AAS? 5. ASA? P Q > > S R ( XWY XVZ ) 6. SSS? 7. SAS? 8. What does CPCTC stand for? Find each value. 9. x = 10. y = 11. m A 12. m E 13. m A 14. m X 15. m ECD 16. m K 17. ABC is isosceles with the vertex angle at C. Find AB.

12 Unit 8 12 Midsegment of Triangle Pythagorean Theorem Triangle Inequality Theorem Triangle Midsegment Theorem 1. Write the equation in slope intercept form of the perpendicular bisector of the segment with endpoints L (4,0) and M ( 2,3). 2. Given that line p is the perpendicular bisector of XZ and XY = 15.5, find ZY. 4. On the balance beam, V is the midpoint of AB and 7 W is the midpoint of YB. The length of VW is 1 8 feet. What is AY? 3. In QRS, QR = 2x + 5, RS = 3x 1, and SQ = 5x. What is the perimeter of the midsegment triangle of QRS? 5. Johnny is attempting to make a triangle with pipe cleaners of lengths 0.5 m, 0.7 m, and 0.3 m. Will he get a triangle? 6. Write the angles of DEF in order from smallest to largest. 7. The lengths of two sides of a triangle are 8.2 m and 3.5 m. Find the range of possible lengths for the third side. 8. x = (Round to nearest hundredth) 9. Will the lengths 15, 18, and 20 make a RIGHT triangle? Why or why not? 10. Given a rectangle with a width of 8 units and a length of 10 units, what is the length of the diagonal of the rectangle? (Round to nearest hundredth) 11. A square has a diagonal of length 10. What is the length of one of the sides of the square? (Round to nearest hundredth) 12. If a 25 foot ladder is placed against a wall so that it reaches a height of 24 feet, how far away from the base of the wall are the feet of the ladder?