Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry M1: Unit 4 Practice Exam

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Which pair of triangles is congruent by ASA?a. c.

b. d.

____ 2. Name the theorem or postulate that lets you immediately conclude ABD CBD.

a. AAS b. SAS c. ASA d. none of these

Name: ________________________ ID: A

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____ 3. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent?

a. SAS only c. either SAS or AASb. AAS only d. neither

____ 4. Based on the given information, what can you conclude, and why?

Given: H L, HJ JL

a. HIJ LKJ by ASA c. HIJ JLK by ASAb. HIJ JLK by SAS d. 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; EDd. No, the two triangles are not congruent.

Name: ________________________ ID: A

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____ 6. Supply the missing reasons to complete the proof.

Given: A D and AC DC

Prove: BC EC

Statement Reasons

1. A D and

AC DC

1. Given

2. BCA ECD 2. Vertical angles are congruent.

3. BCA ECD 3. ?

4. BC EC 4. ?

a. SAS; Corresp. parts of are . c. AAS; Corresp. parts of are .b. ASA; Corresp. parts of are . d. ASA; Substitution

Name: ________________________ ID: A

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____ 7. What is the missing reason in the proof?

Given: ABCD with diagonal BDProve: ABD CDB

Statements Reasons

1. AD BC 1. Definition of parallelogram

2. ADB CBD 2. Alternate Interior Angles Theorem

3. AB CD 3. Definition of parallelogram

4. ABD CDB 4. ?

5. DB DB 5. Reflexive Property of Congruence

6. ABD CDB 6. ASA

a. Alternate Interior Angles Theorem c. Definition of parallelogramb. ASA d. Reflexive Property of Congruence

____ 8. WXYZ is a parallelogram. Name an angle congruent to XWZ.

a. XYW b. XYZ c. WYZ d. WXY

Name: ________________________ ID: A

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____ 9. Justify the last two steps of the proof.

Given: AB DC and AC DBProve: ABC DCB

Proof:

1. AB DC 1. Given

2. AC DB 2. Given

3. BC CB 3. ?

4. ABC DCB 4. ?

a. Symmetric Property of ; SAS c. Reflexive Property of ; SSSb. Reflexive Property of ; SAS d. Symmetric Property of ; SSS

____ 10. Name the angle included by the sides MP and PN .

a. P b. N c. M d. none of these

Name: ________________________ ID: A

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____ 11. 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. CBA CDA d. AB AD

____ 12. State whether ABC and AED are congruent. Justify your answer.

a. yes, by either SSS or SASb. yes, by SAS onlyc. yes, by SSS onlyd. No; there is not enough information to conclude that the triangles are congruent.

____ 13. Which triangles are congruent by ASA?

a. VTU andHGF c. VTU andABCb. none d. ABC andTUV

Name: ________________________ ID: A

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____ 14. Which two triangles are congruent by ASA?

MR bisects QO, andMQP ROP.

a. none c. MQP andMPN

b. MNP andONP d. MPQ andRPO

____ 15. What is the missing reason in the two-column proof?

Given: MO

bisects PMN and OM

bisects PONProve: PMO NMO

Statements Reasons

1. MO

bisects PMN 1. Given2. PMO NMO 2. Definition of angle bisector

3. MO MO 3. Reflexive property

4. OM

bisects PON 4. Given5. POM NOM 5. Definition of angle bisector6. PMO NMO 6. ?

a. ASA Postulate c. SAS Postulateb. AAS Theorem d. 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 ASAb. HL and AAS d. HL, AAS, and ASA

Name: ________________________ ID: A

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____ 17. Find the values of the variables in the parallelogram. The diagram is not to scale.

a. x 58, y 20, z 102 c. x 20, y 58, z 122

b. x 20, y 58, z 102 d. 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. 91 d. 23

Name: ________________________ ID: A

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____ 20. ABCD is a parallelogram. If mCDA 74, then mDAB ? . The diagram is not to scale.

a. 116 b. 148 c. 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 d. 19

____ 22. ABCD is a parallelogram. If mBCD 108, then mDAB ? . The diagram is not to scale.

a. 82 b. 138 c. 108 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. x = 26, y = 9 d. x = 8, y = 23

Name: ________________________ ID: A

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____ 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. x = 6, NM = 19, OL = 19 c. x = 8, NM = 21, OL = 21b. x = 6, NM = 21, OL = 19 d. 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. 6 d. 3

Name: ________________________ ID: A

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____ 27. In the figure, the horizontal lines are parallel and AB BC CD. Find KL and FG. The diagram is not to scale.

a. KL = 7.3, FG = 7.3 c. KL = 7.7, FG = 7.3b. KL = 7.7, FG = 7.7 d. KL 7.3, FG 7.7

ID: A

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Geometry M1: Unit 4 Practice ExamAnswer 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 TheoremSTA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASAKEY: 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 TheoremSTA: 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 TheoremSTA: 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 TheoremSTA: 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.4.6TOP: 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.4.6TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent KEY: ASA | corresponding parts | proofDOK: DOK 2

7. ANS: A PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 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

ID: A

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8. ANS: B PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 PostulatesSTA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 1 Using SSSKEY: 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 PostulatesSTA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SASKEY: 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 PostulatesSTA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 2 Using SASKEY: 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 PostulatesSTA: MA.912.G.4.3| MA.912.G.4.6 TOP: 4-2 Problem 3 Identifying Congruent TrianglesKEY: 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 TheoremSTA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASAKEY: 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 TheoremSTA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5 TOP: 4-3 Problem 1 Using ASAKEY: 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 TheoremSTA: 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 | proofDOK: DOK 2

16. ANS: B PTS: 1 DIF: L3 REF: 4-6 Congruence in Right TrianglesOBJ: 4-6.1 Prove right triangles congruent using the Hypotenuse-Leg TheoremSTA: 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

ID: A

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17. ANS: B PTS: 1 DIF: L4 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: parallelogram | opposite angles | consecutive angles | transversal DOK: DOK 2

18. ANS: A PTS: 1 DIF: L4 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: parallelogram | anglesDOK: DOK 2

19. ANS: B PTS: 1 DIF: L4 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: parallelogram | anglesDOK: DOK 2

20. ANS: D PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: parallelogram | consecutive anglesDOK: DOK 1

21. ANS: C PTS: 1 DIF: L4 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: algebra | parallelogram | opposite angles | consecutive angles DOK: DOK 2

22. ANS: C PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 1 Using Consecutive Angles KEY: parallelogram | opposite anglesDOK: DOK 1

23. ANS: B PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 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 3 Using Algebra to Find Lengths KEY: transversal | diagonal | parallelogram | algebra DOK: DOK 2

24. ANS: D PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 3 Using Algebra to Find Lengths KEY: parallelogram | diagonalDOK: DOK 1

25. ANS: A PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 3 Using Algebra to Find Lengths KEY: parallelogram | algebra DOK: DOK 2

ID: A

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26. ANS: A PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 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 4 Using Parallel Lines and Transversals KEY: transversal | parallel linesDOK: DOK 2

27. ANS: C PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 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 4 Using Parallel Lines and Transversals KEY: parallel lines | transversalDOK: DOK 1