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Chapter 4 Practice Test Geometry Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Use the information given in the diagram. Tell why A B D a. b. c. d. ____ C Reflexive Property, Given Transitive Property, Reflexive Property Given, Reflexive Property Reflexive Property, Transitive Property 2. a. ____ b. c. d° g 5 b f° e° 4 52° 3 a. 4 ____ d. 3. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. 38° ____ and 4. Given a. 2 5. Given a. 22 c b. 5 c. 3 and , find the length of QS and TV. c. 8 d. 20 b. 9 and b. 11 d. 38 , find c. 10 and d. 25 ____ 6. Justify the last two steps of the proof. Given: and Prove: R S T U Proof: 1. 1. Given 2. Given 3. 4. 2. 3. 4. a. Symmetric Property of ; SSS b. Reflexive Property of ; SAS ____ 7. State whether and are congruent. Justify your answer. 7 a. b. c. d. ____ c. Reflexive Property of ; SSS d. Symmetric Property of ; SAS 7 yes, by either SSS or SAS yes, by SSS only yes, by SAS only No; there is not enough information to conclude that the triangles are congruent. 8. Name the angle included by the sides N and M P a. b. c. d. none of these ____ 9. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. ____ 10. From the information in the diagram, can you prove a. yes, by ASA b. yes, by AAA ? Explain. c. yes, by SAS d. no ____ 11. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent? a. either ASA or AAS b. ASA only c. AAS only d. Neither ____ 12. Based on the given information, what can you conclude, and why? Given: I K J H L a. b. by ASA by SAS c. d. by ASA by SAS ____ 13. Name the theorem or postulate that lets you immediately conclude | A D | B C a. SAS b. ASA c. AAS ____ 14. Supply the missing reasons to complete the proof. Given: and Prove: Q S R P a. ASA; Substitution b. SAS; CPCTC T c. AAS; CPCTC d. ASA; CPCTC d. none of these ____ 15. Find the values of x and y. ( ( A | | y° x° B 47° D C Drawing not to scale a. b. c. d. ____ 16. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units? 38° 21 21 Drawing not to scale a. 71° b. 142° c. 152° d. 76° ____ 17. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°? a. 69° b. 84° c. 138° d. 96° ____ 18. Use the information in the figure. Find | E D | 116° F Drawing not to scale a. 32° b. 122° ____ 19. Find the value of x. The diagram is not to scale. c. 64° d. 58° | | S (3 x – 50)° (7 x )° R T a. U b. c. d. none of these c. 16 d. 19 ____ 20. Find the value of x. The diagram is not to scale. Given: , S R U T a. 14 b. 152 ____ 21. The sides of an isosceles triangle have lengths , . The base has length of the base? a. 18 c. 12 b. 4 d. cannot be determined Short Answer 22. . List the six pairs of congruent corresponding parts. Q P S R T 23. Based on the given information, can you conclude that Given: , , and ? Explain. . What is the length 24. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof. Given: Prove: B C A D 25. Is by HL? If so, name the legs that allow the use of HL. P Q S R 26. Write the missing reasons to complete the flow proof. Given: Prove: are right angles, B ( ) A D C 27.Can you conclude the triangles are congruent? Justify your answer. 28. Complete the proof by providing the missing reasons. Given: Prove: , C D B E A Statement 1. 2. 3. 4. 5. , , and are right angles Essay 29. Write a two-column proof. Given: and Prove: B D C A E Reason 1. Given 2. Definition of perpendicular segments 3. ? 4. ? 5. ? 30. Write a two-column proof: Given: Prove: B C A D Other 31. Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence statement and explain. If no, write not possible and tell what other information you would need. ( Given: A B C ( D Chapter 4 Practice Test Geometry Answer Section MULTIPLE CHOICE (2 points each question) 1. ANS: A REF: 4-1 Congruent Figures 2. ANS: D REF: 4-1 Congruent Figures 3. ANS: C REF: 4-1 Congruent Figures 4. ANS: C REF: 4-1 Congruent Figures 5. ANS: C REF: 4-1 Congruent Figures 6. ANS: C REF: 4-2 Triangle Congruence by SSS and SAS 7. ANS: A REF: 4-2 Triangle Congruence by SSS and SAS 8. ANS: A REF: 4-2 Triangle Congruence by SSS and SAS 9. ANS: B REF: 4-3 Triangle Congruence by ASA and AAS 10. ANS: A REF: 4-3 Triangle Congruence by ASA and AAS 11. ANS: A REF: 4-3 Triangle Congruence by ASA and AAS 12. ANS: A REF: 4-3 Triangle Congruence by ASA and AAS 13. ANS: A REF: 4-3 Triangle Congruence by ASA and AAS 14. ANS: D REF: 4-4 Using Congruent Triangles: CPCTC 15. ANS: D REF: 4-5 Isosceles and Equilateral Triangles 16. ANS: A REF: 4-5 Isosceles and Equilateral Triangles 17.ANS: D REF: 4-5 Isosceles and Equilateral Triangles 18. ANS: A REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Example 2 19. ANS: A REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Example 2 20. ANS: A REF: 4-5 Isosceles and Equilateral Triangles TOP: 4-5 Example 2 21. ANS: A REF: 4-5 Isosceles and Equilateral Triangles SHORT ANSWER ( 10 points each problem) 22. ANS: Sides: Angles: , , , , REF: 4-1 Congruent Figures TOP: 4-1 Example 1 23. ANS: Answers may vary. Sample: Two pairs of sides are congruent, but the angle is not included. There is no SSA Congruence Theorem, so you cannot conclude with the information given. REF: 4-2 Triangle Congruence by SSS and SAS 24. ANS: Answers may vary. Sample: Since the two triangles share the side by CPCTC. REF: 4-4 Using Congruent Triangles: CPCTC 25. ANS: Yes, , they are congruent by SAS. Then TOP:4-4 Example 2 (in each triangle) REF: 4-6 Congruence in Right Triangles TOP: 4-6 Example 1 26. ANS: a. Definition of right triangles b. Converse of Isosceles Triangle Theorem c. Reflexive property d. Angle-Angle-Side Congruence Theorem REF: 4-6 Congruence in Right Triangles TOP: 4-6 Example 2 27. ANS: Yes, the diagonal segment is congruent to itself, so the triangles are congruent by SAS. REF: 4-1 Congruent Figures TOP: 4-1 Example 3 28. ANS: Step 3: All right angles are congruent. Step 4: Reflexive Property Step 5. HL Theorem REF: 4-7 Using Corresponding Parts of Congruent Triangles TOP: 4-7 Example 2 ESSAY ( 10 points each problem) 29. ANS: [4] Statement and 1. 2. 3. 4. [3] [2] [1] Reason 1. Given 2. Vertical angles are congruent. 3. SAS 4. CPCTC correct idea, some details inaccurate correct idea, not well organized correct idea, one or more significant steps omitted REF: 4-4 Using Congruent Triangles: CPCTC 30. ANS: [4] Statement 1. Reason and 2. 3. 4. [3] [2] [1] 1. Given 2. Reflexive Property 3. ASA 4. CPCTC correct idea, some details inaccurate correct idea, not well organized correct idea, one or more significant steps omitted REF: 4-4 Using Congruent Triangles: CPCTC OTHER ( 10 points each problem) 31. ANS: Not possible; you have one pair of congruent angles and one pair of congruent sides , but you would need to know that one more pair of angles are congruent, either or , to prove the triangles congruent by AAS. REF: 4-3 Triangle Congruence by ASA and AAS TOP: 4-3 Example 3