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Name: ________________________ Class: ___________________ Date: __________ Geometry M1: Unit 4 Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Which pair of triangles is congruent by ASA? a. b. ____ c. d. 2. Name the theorem or postulate that lets you immediately conclude ABD CBD. a. AAS b. SAS c. 1 ASA d. none of these ID: A Name: ________________________ ____ 3. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent? a. b. ____ SAS only AAS only c. d. either SAS or AAS neither 4. Based on the given information, what can you conclude, and why? Given: H L, HJ JL a. b. ____ ID: A HIJ LKJ by ASA HIJ JLK by SAS c. d. HIJ JLK by ASA HIJ LKJ by SAS 5. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. mR 70, mS 80, mF 70, mD 30, 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 Name: ________________________ ____ ID: A 6. Supply the missing reasons to complete the proof. Given: A D and AC DC Prove: BC EC Statement 1. A D and Reasons 1. Given AC DC 2. BCA ECD 2. Vertical angles are congruent. 3. BCA ECD 3. ? 4. BC EC 4. ? a. b. SAS; Corresp. parts of are . ASA; Corresp. parts of are . c. d. 3 AAS; Corresp. parts of are . ASA; Substitution Name: ________________________ ____ ID: A 7. What is the missing reason in the proof? Given: ABCD with diagonal BD Prove: ABD CDB Statements Reasons 1. Definition of parallelogram 1. AD BC 2. ADB CBD 3. AB CD 4. ABD CDB 5. DB DB 6. ABD CDB a. b. ____ 2. Alternate Interior Angles Theorem 3. Definition of parallelogram 4. ? 5. Reflexive Property of Congruence 6. ASA Alternate Interior Angles Theorem ASA c. d. Definition of parallelogram Reflexive Property of Congruence 8. WXYZ is a parallelogram. Name an angle congruent to XWZ. a. XYW b. XYZ c. 4 WYZ d. WXY Name: ________________________ ____ ID: A 9. Justify the last two steps of the proof. Given: AB DC and AC DB Prove: ABC DCB Proof: 1. AB DC 2. AC DB 3. BC CB 4. ABC DCB a. b. 1. Given 2. Given 3. ? 4. ? Symmetric Property of ; SAS Reflexive Property of ; SAS c. d. Reflexive Property of ; SSS Symmetric Property of ; SSS ____ 10. Name the angle included by the sides MP and PN . a. P b. N c. 5 M d. none of these Name: ________________________ ID: A ____ 11. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate? a. b. AB AD CBA CDA c. d. BAC DAC AB AD ____ 12. State whether ABC and AED are congruent. Justify your answer. a. b. c. d. yes, by either SSS or SAS yes, by SAS only yes, by SSS only No; there is not enough information to conclude that the triangles are congruent. ____ 13. Which triangles are congruent by ASA? a. b. VTU and HGF none c. d. 6 VTU and ABC ABC and TUV Name: ________________________ ID: A ____ 14. Which two triangles are congruent by ASA? MR bisects QO, and MQP ROP. a. b. none MNP and ONP c. d. MQP and MPN MPQ and RPO ____ 15. What is the missing reason in the two-column proof? Given: MO bisects PMN and OM bisects PON Prove: PMO NMO Statements Reasons 1. MO bisects PMN 2. PMO NMO 3. MO MO 1. Given 2. Definition of angle bisector 3. Reflexive property 4. OM bisects PON 5. POM NOM 6. PMO NMO a. b. ASA Postulate AAS Theorem 4. Given 5. Definition of angle bisector 6. ? c. d. SAS Postulate SSS Postulate ____ 16. YX is a perpendicular bisector 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 immediately conclude that WXY ZXY? a. HL, AAS, ASA, SAS, and SSS c. HL and ASA b. HL and AAS d. HL, AAS, and ASA 7 Name: ________________________ ID: A ____ 17. Find the values of the variables in the parallelogram. The diagram is not to scale. a. b. x 58, y 20, z 102 x 20, y 58, z 102 c. d. x 20, y 58, z 122 x 58, y 58, z 122 ____ 18. In the parallelogram, mKLO 43 and mMLO 69. Find mKJM. The diagram is not to scale. a. 112 b. 102 c. 43 d. 68 ____ 19. In the parallelogram, mQRP 23 and mPRS 91. Find mPQR. The diagram is not to scale. a. 114 b. 66 c. 8 91 d. 23 Name: ________________________ ID: A ____ 20. ABCD is a parallelogram. If mCDA 74, then mDAB a. 116 b. 148 c. ? . The diagram is not to scale. 74 d. 106 ____ 21. For the parallelogram, if m2 4x 26 and m4 3x 7, find m1. The diagram is not to scale. a. 50 b. 140 c. 130 ____ 22. ABCD is a parallelogram. If mBCD 108, then mDAB a. 82 b. 138 c. d. ? 108 19 . The diagram is not to scale. d. 72 ____ 23. In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 2x – 4, and HE = 5y + 2. Find the values of x and y. The diagram is not to scale. a. x = 9, y = 26 b. x = 23, y = 8 c. 9 x = 26, y = 9 d. x = 8, y = 23 Name: ________________________ ID: A ____ 24. Find AM in the parallelogram if PN =13 and AO = 4. The diagram is not to scale. a. 13 b. 6.5 c. 8 d. 4 ____ 25. LMNO is a parallelogram. If NM = x + 13 and OL = 2x + 7, find the value of x and then find NM and OL. a. b. x = 6, NM = 19, OL = 19 x = 6, NM = 21, OL = 19 c. d. x = 8, NM = 21, OL = 21 x = 8, NM = 19, OL = 21 ____ 26. In the figure, the horizontal lines are parallel and AB BC CD. Find JM. The diagram is not to scale. a. 9 b. 12 c. 10 6 d. 3 Name: ________________________ ID: A ____ 27. In the figure, the horizontal lines are parallel and AB BC CD. Find KL and FG. The diagram is not to scale. a. b. KL = 7.3, FG = 7.3 KL = 7.7, FG = 7.7 c. d. 11 KL = 7.7, FG = 7.3 KL 7.3, FG 7.7 ID: A Geometry M1: Unit 4 Practice Exam Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA KEY: ASA DOK: DOK 1 2. ANS: C PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent KEY: ASA | AAS | SAS DOK: DOK 2 3. ANS: B PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent KEY: ASA | AAS | reasoning DOK: DOK 2 4. ANS: A PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent KEY: ASA | reasoning DOK: DOK 2 5. ANS: A PTS: 1 DIF: L3 REF: 4-4 Using Corresponding Parts of Congruent Triangles OBJ: 4-4.1 Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6 TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent KEY: ASA | corresponding parts | word problem DOK: DOK 2 6. ANS: B PTS: 1 DIF: L3 REF: 4-4 Using Corresponding Parts of Congruent Triangles OBJ: 4-4.1 Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles are congruent STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6 TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent KEY: ASA | corresponding parts | proof DOK: DOK 2 7. ANS: A PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: 6-2.2 Use relationships among diagonals of parallelograms STA: MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 TOP: 6-2 Problem 2 Using Properties of Parallelograms in a Proof KEY: proof | two-column proof | parallelogram | diagonal DOK: DOK 2 1 ID: A 8. ANS: B PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms OBJ: 6-2.1 Use relationships among sides and angles of parallelograms STA: MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 TOP: 6-2 Problem 2 Using Properties of Parallelograms in a Proof KEY: parallelogram | opposite angles DOK: DOK 1 9. ANS: C PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 1 Using SSS KEY: SSS | reflexive property | proof DOK: DOK 2 10. ANS: A PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS KEY: angle DOK: DOK 1 11. ANS: D PTS: 1 DIF: L4 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SAS KEY: SAS | reasoning DOK: DOK 2 12. ANS: A PTS: 1 DIF: L3 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates STA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 3 Identifying Congruent Triangles KEY: SSS | SAS | reasoning DOK: DOK 2 13. ANS: C PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA KEY: ASA DOK: DOK 1 14. ANS: D PTS: 1 DIF: L4 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASA KEY: ASA | vertical angles DOK: DOK 2 15. ANS: A PTS: 1 DIF: L3 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 2 Writing a Proof Using ASA KEY: ASA | proof DOK: DOK 2 16. ANS: B PTS: 1 DIF: L3 REF: 4-6 Congruence in Right Triangles OBJ: 4-6.1 Prove right triangles congruent using the Hypotenuse-Leg Theorem STA: MA.912.G.2.3| MA.912.G.4.6| MA.912.G.5.4 TOP: 4-6 Problem 1 Using the HL Theorem KEY: right triangle | HL Theorem | ASA | SAS | AAS | SSS | proof | word problem | problem solving | reasoning DOK: DOK 2 2 ID: A 17. ANS: OBJ: STA: TOP: KEY: DOK: 18. ANS: OBJ: STA: TOP: DOK: 19. ANS: OBJ: STA: TOP: DOK: 20. ANS: OBJ: STA: TOP: DOK: 21. ANS: OBJ: STA: TOP: KEY: DOK: 22. ANS: OBJ: STA: TOP: DOK: 23. ANS: OBJ: STA: TOP: KEY: 24. ANS: OBJ: STA: TOP: DOK: 25. ANS: OBJ: STA: TOP: DOK: B PTS: 1 DIF: L4 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles parallelogram | opposite angles | consecutive angles | transversal DOK 2 A PTS: 1 DIF: L4 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles KEY: DOK 2 B PTS: 1 DIF: L4 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles KEY: DOK 2 D PTS: 1 DIF: L2 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles KEY: DOK 1 C PTS: 1 DIF: L4 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles algebra | parallelogram | opposite angles | consecutive angles DOK 2 C PTS: 1 DIF: L2 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 1 Using Consecutive Angles KEY: DOK 1 B PTS: 1 DIF: L3 REF: 6-2.2 Use relationships among diagonals of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 3 Using Algebra to Find Lengths transversal | diagonal | parallelogram | algebra DOK: D PTS: 1 DIF: L2 REF: 6-2.2 Use relationships among diagonals of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 3 Using Algebra to Find Lengths KEY: DOK 1 A PTS: 1 DIF: L2 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 3 Using Algebra to Find Lengths KEY: DOK 2 3 6-2 Properties of Parallelograms 6-2 Properties of Parallelograms parallelogram | angles 6-2 Properties of Parallelograms parallelogram | angles 6-2 Properties of Parallelograms parallelogram | consecutive angles 6-2 Properties of Parallelograms 6-2 Properties of Parallelograms parallelogram | opposite angles 6-2 Properties of Parallelograms DOK 2 6-2 Properties of Parallelograms parallelogram | diagonal 6-2 Properties of Parallelograms parallelogram | algebra ID: A 26. ANS: OBJ: STA: TOP: DOK: 27. ANS: OBJ: STA: TOP: DOK: A PTS: 1 DIF: L3 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 4 Using Parallel Lines and Transversals KEY: DOK 2 C PTS: 1 DIF: L2 REF: 6-2.1 Use relationships among sides and angles of parallelograms MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5 6-2 Problem 4 Using Parallel Lines and Transversals KEY: DOK 1 4 6-2 Properties of Parallelograms transversal | parallel lines 6-2 Properties of Parallelograms parallel lines | transversal