Geometry Ch 4 Practice Exam

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1 Name: Class: Date: Geometry Ch 4 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. If BCDE is congruent to OPQR, then BC is congruent to?. a. OP b. PQ c. OR d. QR 2. If MNO PQR, which of the following can you NOT conclude as being true? a. N Q b. NO QR c. M P d. MN PR 3. Given ABC PQR, m B = 2v + 3, and m Q = 5v 6, find m B and m Q. a. 9 b. 24 c. 10 d Justify the last two steps of the proof. Given: MN PO and MO PN Prove: MNO PON Proof: 1. MN PO 1. Given 2. MO PN 2. Given 3. NO ON 3.? 4. MNO PON 4.? a. Symmetric Property of ; SSS c. Reflexive Property of ; SAS b. Reflexive Property of ; SSS d. Symmetric Property of ; SAS 1

2 Name: 5. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? a. AB AD c. BAC DAC b. AB AD d. CBA CDA 6. State whether ABC and AED are congruent. Justify your answer. a. yes, by either SSS or SAS b. yes, by SSS only c. yes, by SAS only d. No; there is not enough information to conclude that the triangles are congruent. 7. Based on the given information, what can you conclude, and why? Given: M Q, MO OQ a. MNO QPO by SAS c. MNO OQP by SAS b. MNO OQP by ASA d. MNO QPO by ASA 2

3 Name: 8. Supply the missing reasons to complete the proof. Given: N Q and NO QO Prove: MO PO Statement 1. N Q and NO QO Reasons 1. Given 2. MON POQ 2. Vertical angles are congruent. 3. MON POQ 3.? 4. MO PO 4.? a. ASA; Substitution c. ASA; CPCTC b. AAS; CPCTC d. SAS; CPCTC 3

4 Name: 9. Supply the reasons missing from the proof shown below. Given: AB AC, BAD CAD Prove: AD bisects BC Statements Reasons 1. AB AC 1. Given 2. BAD CAD 2. Given 3. AD AD 3. Reflexive Property 4. BAD CAD 4.? 5. BD CD 5.? 6. AD bisects BC 6. Def. of segment bisector a. ASA; CPCTC c. SSS; Reflexive Property b. SAS; Reflexive Property d. SAS; CPCTC 10. Find the values of x and y. a. x = 90, y = 37 c. x = 53, y = 37 b. x = 90, y = 53 d. x = 37, y = 53 4

5 Name: 11. The octagon in the figure is equiangular and AB AC. Find m ACB. a. 135 b. 45 c. 30 d What is the measure of a base angle of an isosceles triangle if the vertex angle measures 48 and the two congruent sides each measure 21 units? a. 142 b. 66 c. 71 d Find the value of x. The diagram is not to scale. a. x = 24 b. x = 30 c. x = 12 d. none of these 5

6 Name: 14. Find the value of x. The diagram is not to scale. Given: RS ST, m RTS = 5x 47, m STU = 6x a. 19 b. 142 c. 21 d What additional information will allow you to prove the triangles congruent by the HL Theorem? a. A E c. AC DC b. m BCE = 90 d. AC BD Short Answer 16. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that D B. 6

7 Name: 17. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof. Given: CB CD, BCA DCA Prove: BA DA 18. 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. Essay 19. Write a proof. Given: BC DA, 1 2, and CF AF Prove: CFE AFE 7

8 Name: 20. Write a two-column proof. Given: BC EC and AC DC Prove: BA ED 8

9 Geometry Ch 4 Practice Exam Answer Section MULTIPLE CHOICE 1. ANS: A 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 2. ANS: D 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 3. ANS: A 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 4. ANS: B 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 5. ANS: B 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 6. ANS: A 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 7. ANS: D 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 reasoning 8. ANS: C 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 9. ANS: D PTS: 1 DIF: L2 STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 1 KEY: segment bisector isosceles triangle proof 10. ANS: A PTS: 1 DIF: L2 STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: angle bisector isosceles triangle 1

10 11. ANS: B PTS: 1 DIF: L3 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 12. ANS: B PTS: 1 DIF: L2 STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: isosceles triangle Converse of Isosceles Triangle Theorem Triangle Angle-Sum Theorem 13. ANS: A PTS: 1 DIF: L3 STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem isosceles triangle 14. ANS: A PTS: 1 DIF: L1 STA: CA GEOM 4.0 CA GEOM 5.0 CA GEOM 12.0 TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem isosceles triangle problem solving Triangle Angle-Sum Theorem 15. ANS: C PTS: 1 DIF: L2 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: HL Theorem right triangle reasoning SHORT ANSWER 16. ANS: Answers may vary. Sample: Because the two triangles share the side AC, they are congruent by SAS. Then D B by CPCTC. 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 2 KEY: CPCTC SAS writing in math reasoning 17. ANS: Answers may vary. Sample: Since the two triangles share the side RP, they are congruent by SAS. Then QP SP by CPCTC. 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 2 KEY: SAS CPCTC writing in math reasoning 18. ANS: Yes; PQS RQS by SAS. PTS: 1 DIF: L3 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 KEY: SAS proof reasoning 2

11 ESSAY 19. ANS: [4] Statement Reason 1. BC DA 1. Given Given 3. BEC DEA 3. Vertical angles are congruent. 4. BEC DEA 4. AAS 5. CE AE 5. CPCTC 6. CF AF 7. EF EF 8. CFE AFE 6. Given 7. Reflexive Property 8. SSS [3] correct idea, some details inaccurate [2] correct idea, not well organized [1] correct idea, one or more significant steps omitted PTS: 1 DIF: L4 REF: 4-7 Using Corresponding Parts of Congruent Triangles OBJ: Using Two Pairs of Congruent Triangles STA: CA GEOM 5.0 TOP: 4-7 Example 3 KEY: AAS CPCTC corresponding parts congruent figures proof rubric-based question extended response 20. ANS: [4] Statement Reason 1. BC EC and AC DC 1. Given 2. BCA ECD 2. Vertical angles are congruent. 3. BCA ECD 3. SAS 4. BA ED 4. CPCTC [3] correct idea, some details inaccurate [2] correct idea, not well organized [1] correct idea, one or more significant steps omitted PTS: 1 DIF: L4 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: Proving Parts of Triangles Congruent STA: CA GEOM 5.0 CA GEOM 6.0 KEY: CPCTC congruent figures proof SAS rubric-based question extended response 3

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