Name: Class: _ Date: _ North Carolina Math 2 Transition Edition Unit 4 Assessment: Similarity and Congruence Multiple Choice Identify the choice that best completes the statement or answers the question. 1. CDE and XYZ are congruent triangles. Which statement is know to be true? a. C Y c. D Z b. E X d. D Y 2. What is a set of equivalent measures that does not make it possible to determine if any two given triangles are congruent? a. side-side-angle c. angle-side-angle b. side-side-side d. angle-angle-side 3. If m 1 = 3x and m 4 = 3x 6 in the diagram below, find m 2 if 3 is a right angle. a. 42 c. 16 b. 138 d. 48 1
Name: 4. In the proof of the Vertical Angles Theorem below, the reasons have been omitted. What is the reason for step 3 of this proof? Refer to the diagram given. In the diagram, 3 and 1 form a linear pair and 1 and 4 form a linear pair. Prove that 3 4. Statements 1. 3 and 1 form a linear pair. 1.? 1 and 4 form a linear pair. 2. 3 and 1 are supplementary. 2.? 1 and 4 are supplementary. 3. 3 4 3.? Reasons a. Given b. Angles supplementary to the same angle or to congruent angles are congruent. c. m 3 + m 1 = 180 m 1 + m 4 = 180 d. Supplement Theorem 5. If m 1 = 5x 9 and m 2 = 7x 3, find m 4 given that lines k and l intersect as shown below. a. 16 c. 115 b. 71 d. 109 2
Name: 6. In the diagram below, is the transversal of the parallel lines m and n. Find m 8 if m 2 = 6x + 18 and m 8 = 12x. a. 72 c. 36 b. 108 d. 9 3
Name: 7. Given two sets of parallel lines in the diagram below, what is the relationship between 1 and 12? a. No relationship exists. b. 1 and 12 are congruent right angles because all right angles are congruent and two pairs of intersecting parallel lines are always perpendicular. c. 1 16 since they are alternate exterior angles and alternate exterior angles are congruent. Then, by corresponding angles, 16 12. Therefore, 1 12 by the Transitive Property. d. 1 and 16 are supplementary since alternate exterior angles are supplementary. Then, by corresponding angles, 16 12. Therefore, 1 and 12 are supplementary because angles that are supplementary to the same or congruent angles are congruent. 8. What is the measure of B? a. 67 c. 113 b. 31 d. 98 4
Name: 9. What is the measure of C? a. 30 c. 15 b. 120 d. 60 10. What is the measure of C? a. 108 c. 36 b. 144 d. 72 5
Name: 11. If AB = 3x + 6 and ZY = 4x 2, what is the length of AB? a. 6 units c. 2 units b. 24 units d. 12 units 12. Determine the scale factor of the dilation below. a. k = 1 4 c. k = 1 8 b. k = 8 d. k = 4 6
Name: 13. Are the two triangles similar? Why or why not? a. They are not similar; ΔABC has undergone a transformation that does not preserve congruency. b. They are not similar; ΔABC has undergone a transformation that does not preserve similarity. c. They are similar; ΔABC has undergone a transformation that preserves similarity. d. They are similar; ΔABC has undergone a transformation that preserves congruency. 14. Identify the similar triangles. a. BCA EFD b. ABC EFD c. ABC FED d. There is not enough information to determine if the triangles are similar. 7
Name: 15. Which statement would justify ΔABC ~ ΔDEF? a. Side-Side-Side (SSS) Similarity Statement b. Side-Angle-Side (SAS) Similarity Statement c. It is not possible to determine if ΔABC ΔDEF. d. Angle-Angle (AA) Similarity Statement 16. Which statement would justify ΔABC ~ ΔADE? a. Angle-Angle (AA) Similarity Statement b. Side-Side-Side (SSS) Similarity Statement c. Side-Angle-Side (SAS) Similarity Statement d. It is not possible to determine if ΔABC ΔADE. 8
Name: 17. ΔABF ~ ΔACE. What is the length of FE? a. 2.7 units b. 37.04 units c. There is not enough information to determine the length of FE. d. 10.8 units 18. What is the length of AD? a. 187.5 units b. 30 units c. There is not enough information to determine the length of AD. d. 8.5 units 9
Name: 19. ΔABC is a right triangle. Find the length of x, which is the altitude of ΔABC. a. 36 units b. 2.3 units c. 7.7 units d. There is not enough information to determine the length of x. 20. ΔABC is a right triangle. What is the length of BD? a. 22 units b. 5.5 units c. 4 units d. There is not enough information to determine the length of BD. 10
North Carolina Math 2 Transition Edition Unit 4 Assessment: Similarity and Congruence Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 REF: MI 5.6 NAT: G-CO.7 TOP: Congruent Triangles KEY: congruent triangles congruent angles angle triangle congruent 2. ANS: A angle-angle-angle PTS: 1 REF: MI 5.6 NAT: G-CO.8 TOP: Congruent Triangles KEY: angle ASA congruent angles congruent sides congruent triangles side SSS triangle SAS equivalent measure 3. ANS: A PTS: 1 REF: MII 5.5 NAT: G-CO.9 TOP: Proving Theorems About Lines and Angles KEY: angle measure vertical angles complementary angles 4. ANS: B PTS: 1 REF: MII 5.5 NAT: G-CO.9 TOP: Proving Theorems About Lines and Angles KEY: Vertical Angles Theorem proof linear pair supplementary angles 5. ANS: D PTS: 1 REF: MII 5.5 NAT: G-CO.9 TOP: Proving Theorems About Lines and Angles KEY: angle measure linear pair supplementary angles adjacent angles vertical angles 6. ANS: B PTS: 1 REF: MII 5.5 NAT: G-CO.9 TOP: Proving Theorems About Lines and Angles KEY: angle measure same-side exterior angles parallel lines transversal MSC: Pre-Assessment 7. ANS: C PTS: 1 REF: MII 5.5 NAT: G-CO.9 TOP: Proving Theorems About Lines and Angles KEY: parallel lines transversal corresponding angles alternate exterior angles alternate interior angles supplementary angles 8. ANS: A PTS: 1 REF: MII 5.6 NAT: G-CO.10 TOP: Proving Theorems About Triangles KEY: triangle angle measure MSC: Pre-Assessment 9. ANS: D PTS: 1 REF: MII 5.6 NAT: G-CO.10 TOP: Proving Theorems About Triangles KEY: angle measure triangle interior angle sum MSC: Pre-Assessment 1
10. ANS: C PTS: 1 REF: MII 5.6 NAT: G-CO.10 TOP: Proving Theorems About Triangles KEY: angle measure angles interior angle sum isosceles triangle triangle 11. ANS: D PTS: 1 REF: MII 5.6 NAT: G-CO.10 TOP: Proving Theorems About Triangles KEY: triangle side length 12. ANS: A PTS: 1 REF: MII 5.2 NAT: G-SRT.1b TOP: Investigating Properties of Dilations KEY: center of dilation dilation enlargement reduction scale factor MSC: Pre-Assessment 13. ANS: C PTS: 1 REF: MII 5.3 NAT: G-SRT.2 TOP: Defining and Applying Similarity KEY: similarity similarity transformation 14. ANS: B PTS: 1 REF: MII 5.3 NAT: G-SRT.3 TOP: Defining and Applying Similarity KEY: similarity proportional Angle-Angle Similarity Statement 15. ANS: C PTS: 1 REF: MII 5.4 NAT: G-SRT.4 TOP: Proving Similarity KEY: Side-Angle-Side similarity similar triangles 16. ANS: B PTS: 1 REF: MII 5.4 NAT: G-SRT.4 TOP: Proving Similarity KEY: Side-Side-Side similarity similar triangles 17. ANS: A PTS: 1 REF: MII 5.4 NAT: G-SRT.4 TOP: Proving Similarity KEY: ratios segment similarity similar triangles 18. ANS: B PTS: 1 REF: MII 5.4 NAT: G-SRT.4 TOP: Proving Similarity KEY: ratios similarity triangle angle bisector 19. ANS: A PTS: 1 REF: MII 5.4 NAT: G-SRT.4 TOP: Proving Similarity KEY: right triangle altitude similarity similar triangles MSC: Pre-Assessment 20. ANS: A PTS: 1 REF: MII 5 NAT: G-SRT.4 TOP: Similarity, Right Triangle Trigonometry, and Proof KEY: similarity right triangle ratios MSC: Unit Assessment 2