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Geometry Honors: Chapter 4 Test Short Answer 1. Are the triangles congruent? Justify your answer. 2. Complete the proof by giving the missing reasons Given: Prove: N F B V Statement 1. 2. Reason 1. Given 3. 4. 5. 3. ? 4. Reflexive Property 5. ? ? 2. ? 3. Supply the missing reasons to complete the proof. Given: and Prove: S U T R V 4. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and name the postulate you would use. If no, write not possible and tell what other information you would need. Q | | ( ) S P R 5. Supply the reasons missing from the proof shown below. Given: , Prove: | | ( ( A B D C 6. Justify the last two steps of the proof. Given: and Prove: xº M N 58° O Drawing not to scale 10. What is the value of x? P E Proof: 1. 1. Given 3. 4. 7. Given | 2. Given 3. 4. 2. xº and , find B | C D | 9. What is the value of x? E | 108.5° F Drawing not to scale and 8. What additional information will allow you to prove the triangles congruent by the HL Theorem? A D 11. 12. Two sides of an equilateral triangle have lengths and . Which could be the length of the third side: or ? 13. If BCDE is congruent to OPQR, then congruent to 5 5 is 14. State whether and are congruent. Justify your answer. 15. What is the missing reason in the two-column proof? Given: Prove: bisects and bisects N < M O > P Statements Reasons 1. 2. 3. 1. Given 2. Definition of angle bisector 3. Reflexive property bisects 4. Given 5. Definition of angle bisector 6. ? 4. bisects 5. 6. 16. What is the value of x? A ( ( 34° 21 | 21 | y° x° xº Drawing not to scale B 65° D C Drawing not to scale 17. Find the values of x and y. 18. The two triangles are congruent as suggested by their appearance. Find the value of g. The diagrams are not to scale. M N d° 30° g 25 b f° e° 24 60° 7 c P 19. Given and , find the length of QS and TV. 20. What else must you know to prove the triangles congruent by ASA? By SAS? 23. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? B A ( A ( C D B 21. What common angle do B C D 24. Find the value of x. The diagram is not to scale. S C A | | F (2 x – 30)° R G 22. Name the angle included by the sides and (8 x )° T U 25. Which triangles are congruent by ASA? F ( A V T )) | | G ) B C D H U A (( B ( C 26. Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement? Multiple Choice Identify the choice that best completes the statement or answers the question. 27. Based on the given information, what can you 28. R, S, and T are the vertices of one triangle. E, F, conclude, and why? and D are the vertices of another triangle. RS Given: = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to F H A. B. C. D. G E A. B. C. D. I by ASA by ASA by SAS by SAS yes, by AAS; yes, by ASA; yes, by SAS; No, the two triangles are not congruent. 29. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent? A. B. C. D. SAS only either SAS or AAS AAS only neither 30. If and , which additional statement does NOT allow you to conclude that ? A. B. C. D. 31. For which situation could you immediately prove A. III only B. II and III C. I only using the HL Theorem? D. II only