Geometry Chap 4 Practice Test Answers

Name: ______________________ Class: _________________ Date: _________ Geo, Chap 4 Practice Test, EV Ver 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. (4-3) In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA? a. c. b. d. ____ 2. (4-4) Supply the missing reasons to complete the proof. Given: ∠Q ≅ ∠T and QR ≅ TR Prove: PR ≅ SR Statement 1. ∠Q ≅ ∠T and Reasons 1. Given QR ≅ TR a. b. ____ 2. ∠PRQ ≅ ∠SRT 2. Vertical angles are congruent. 3. ΔPRQ ≅ ΔSRT 3. ? 4. PR ≅ SR 4. ? AAS; CPCTC SAS; CPCTC c. d. ASA; Substitution ASA; CPCTC 3. (4-4) R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m∠R = 80, m∠S = 60, m∠F = 80, m∠D = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to RT. a. yes, by ASA; FD b. yes, by AAS; ED c. d. yes, by SAS; ED No, the two triangles are not congruent. Short Answer 4. (4-1) If BCDE is congruent to OPQR, then BC is congruent to ? . 5. (4-1) In the paper airplane, ABCD ≅ EFGH, m∠B = m∠BCD = 90, and m∠BAD = 126. Find m∠GHE. 6. (4-1) Given ΔQRS ≅ ΔTUV, QS = 5v + 2, and TV = 8v − 7, find the length of QS and TV. 7. (4-2) Justify the last two steps of the proof. Given: AB ≅ DC and AC ≅ DB Prove: ΔABC ≅ ΔDCB Proof: 1. AB ≅ DC 2. AC ≅ DB 3. BC ≅ CB 4. ΔABC ≅ ΔDCB 1. Given 2. Given 3. ? 4. ? 8. (4-2) What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? 9. (4-2) State whether ΔABC and ΔAED are congruent. Justify your answer. 10. (4-3) What is the missing reason in the two-column proof? ⎯⎯ → ⎯⎯ → Given: AC bisects ∠DAB and CA bisects ∠DCB Prove: ΔDAC ≅ ΔBAC Statements Reasons 1. AC bisects ∠DAB 2. ∠DAC ≅ ∠BAC 3. AC ≅ AC 1. Given 2. Definition of angle bisector 3. Reflexive property 4. CA bisects ∠DCB 5. ∠DCA ≅ ∠BCA 6. ΔDAC ≅ ΔBAC 4. Given 5. Definition of angle bisector 6. ? ⎯⎯ → ⎯⎯ → 11. (4-3) From the information in the diagram, can you prove ΔFDG ≅ ΔFDE? Explain. 12. (4-5) Find the values of x and y. 13. (4-5) The octagon in the figure is equiangular and AB ≅ AC. Find m∠ACB. 14. (4-5) Two sides of an equilateral triangle have lengths 3x + 4 and 2x + 8. Which of 20 − x or 6x + 1 could be the length of the third side? 15. (4-6) YX is perpendicular to WZ at X between W and Z. ∠ZWY ≅ ∠WZY. By which of the five congruence statements, HL, AAS, ASA, SAS, and SSS, can you conclude that ΔWXY ≅ ΔZXY? Geo, Chap 4 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: A 2. ANS: D 3. ANS: A KEY: ASA KEY: ASA | CPCTC | proof KEY: ASA | CPCTC | word problem SHORT ANSWER 4. ANS: OP KEY: congruent figures | corresponding parts | word problem 5. ANS: 54 KEY: congruent figures | corresponding parts 6. ANS: 17 Reflexive Property of ≅; SSS 7. ANS: KEY: SSS | reflexive property | proof 8. ANS: AC ⊥ BD KEY: SAS | reasoning 9. ANS: yes, by either SSS or SAS KEY: SSS | SAS | reasoning 10. ANS: ASA Postulate KEY: ASA | proof 11. ANS: yes, by ASA KEY: ASA | reasoning 12. ANS: x = 90, y = 27 KEY: angle bisector | isosceles triangle 13. ANS: 45 KEY: isosceles triangle | Isosceles Triangle Theorem | Polygon Angle-Sum Theorem 14. ANS: 20 – x only KEY: equilateral triangle | word problem | problem solving 15. ANS: HL and AAS KEY: right triangle | HL Theorem | ASA | SAS | AAS | SSS | proof | word problem | problem solving | reasoning