Geo, Chap 4 Practice Test, EV Ver 1
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1 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. 1
2 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 QR TR Reasons 1. Given 2. PRQ SRT 2. Vertical angles are congruent. 3. ΔPRQ ΔSRT 3.? 4. PR SR 4.? a. AAS; CPCTC c. ASA; Substitution b. SAS; CPCTC d. 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. yes, by SAS; ED d. No, the two triangles are not congruent. 2
3 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. 3
4 7. (4-2) Justify the last two steps of the proof. Given: AB DC and AC DB Prove: ΔABC ΔDCB Proof: 1. AB DC 1. Given 2. AC DB 2. Given 3. BC CB 3.? 4. ΔABC ΔDCB 4.? 8. (4-2) What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? 4
5 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 1. Given 2. DAC BAC 2. Definition of angle bisector 3. AC AC 3. Reflexive property 4. CA bisects DCB 4. Given 5. DCA BCA 5. Definition of angle bisector 6. ΔDAC ΔBAC 6.? 5
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. 6
7 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? 7
8 Geo, Chap 4 Practice Test, EV Ver 1 Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-3 Example 1 KEY: ASA 2. ANS: D PTS: 1 DIF: L2 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: Proving Parts of Triangles Congruent STA: CA GEOM 5.0 CA GEOM 6.0 TOP: 4-4 Example 1 KEY: ASA CPCTC proof 3. ANS: A PTS: 1 DIF: L3 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: Proving Parts of Triangles Congruent STA: CA GEOM 5.0 CA GEOM 6.0 TOP: 4-4 Example 1 KEY: ASA CPCTC word problem SHORT ANSWER 4. ANS: OP PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: Congruent Figures STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-1 Example 1 KEY: congruent figures corresponding parts word problem 5. ANS: 54 PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: Congruent Figures STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-1 Example 2 KEY: congruent figures corresponding parts 6. ANS: 17 PTS: 1 DIF: L3 REF: 4-1 Congruent Figures OBJ: Congruent Figures STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 KEY: congruent figures corresponding parts 7. ANS: Reflexive Property of ; SSS PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Using the SSS and SAS Postulates STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-2 Example 1 KEY: SSS reflexive property proof 1
9 8. ANS: AC BD PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Using the SSS and SAS Postulates STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-2 Example 2 KEY: SAS reasoning 9. ANS: yes, by either SSS or SAS PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: Using the SSS and SAS Postulates STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-2 Example 3 KEY: SSS SAS reasoning 10. ANS: ASA Postulate PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-3 Example 4 KEY: ASA proof 11. ANS: yes, by ASA PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-3 Example 3 KEY: ASA reasoning 12. ANS: x = 90, y = 27 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: The Isosceles Triangle Theorems STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: angle bisector isosceles triangle 13. ANS: 45 PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: The Isosceles Triangle Theorems STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 3 KEY: isosceles triangle Isosceles Triangle Theorem Polygon Angle-Sum Theorem 14. ANS: 20 x only PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: The Isosceles Triangle Theorems STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 KEY: equilateral triangle word problem problem solving 2
10 15. ANS: HL and AAS PTS: 1 DIF: L3 REF: 4-6 Congruence in Right Triangles OBJ: The Hypotenuse-Leg Theorem STA: CA GEOM 2.0 CA GEOM 5.0 TOP: 4-6 Example 1 KEY: right triangle HL Theorem ASA SAS AAS SSS proof word problem problem solving reasoning 3
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