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

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Geometry Ch 4 Practice Exam

Multiple ChoiceIdentify 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, mB = 2v + 3, and mQ = 5v 6, find mB and mQ.a. 9 b. 24 c. 10 d. 21

____ 4. Justify the last two steps of the proof.Given: MN PO and MO PNProve: MNO PON

Proof:1. MN PO 1. Given2. MO PN 2. Given3. NO ON 3. ?4. MNO PON 4. ?

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

Name: ________________________ ID: A

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____ 5. What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate?

a. AB AD c. BAC DACb. AB AD d. CBA CDA

____ 6. State whether ABC and AED are congruent. Justify your answer.

a. yes, by either SSS or SASb. yes, by SSS onlyc. yes, by SAS onlyd. 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 SASb. MNO OQP by ASA d. MNO QPO by ASA

Name: ________________________ ID: A

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____ 8. Supply the missing reasons to complete the proof.Given: N Q and NO QOProve: MO PO

Statement Reasons

1. N Q andNO QO

1. Given

2. MON POQ 2. Vertical angles are congruent.3. MON POQ 3. ?4. MO PO 4. ?

a. ASA; Substitution c. ASA; CPCTCb. AAS; CPCTC d. SAS; CPCTC

Name: ________________________ ID: A

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____ 9. Supply the reasons missing from the proof shown below.Given: AB AC , BAD CADProve: 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 bisectora. ASA; CPCTC c. SSS; Reflexive Propertyb. SAS; Reflexive Property d. SAS; CPCTC

____ 10. Find the values of x and y.

a. x = 90, y = 37 c. x = 53, y = 37b. x = 90, y = 53 d. x = 37, y = 53

Name: ________________________ ID: A

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____ 11. The octagon in the figure is equiangular and AB AC. Find mACB.

a. 135 b. 45 c. 30 d. 90

____ 12. 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. 132

____ 13. Find the value of x. The diagram is not to scale.

a. x = 24 b. x = 30 c. x = 12 d. none of these

Name: ________________________ ID: A

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____ 14. Find the value of x. The diagram is not to scale.

Given: RS ST, mRTS = 5x 47, mSTU = 6x

a. 19 b. 142 c. 21 d. 24

____ 15. What additional information will allow you to prove the triangles congruent by the HL Theorem?

a. A E c. AC DCb. mBCE = 90 d. AC BD

Short Answer

16. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that D B.

Name: ________________________ ID: A

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17. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof.

Given: CB CD, BCA DCAProve: 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 AFProve: CFE AFE

Name: ________________________ ID: A

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20. Write a two-column proof.Given: BC EC and AC DCProve: BA ED

ID: A

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Geometry Ch 4 Practice ExamAnswer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L2 REF: 4-1 Congruent FiguresOBJ: 4-1.1 Congruent Figures STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0TOP: 4-1 Example 1 KEY: congruent figures | corresponding parts | word problem

2. ANS: D PTS: 1 DIF: L2 REF: 4-1 Congruent FiguresOBJ: 4-1.1 Congruent Figures STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0TOP: 4-1 Example 1 KEY: congruent figures | corresponding parts | word problem

3. ANS: A PTS: 1 DIF: L3 REF: 4-1 Congruent FiguresOBJ: 4-1.1 Congruent Figures STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0KEY: congruent figures | corresponding parts

4. ANS: B PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Using the SSS and SAS Postulates STA: CA GEOM 2.0| CA GEOM 5.0TOP: 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: 4-2.1 Using the SSS and SAS Postulates STA: CA GEOM 2.0| CA GEOM 5.0TOP: 4-2 Example 2 KEY: SAS | reasoning

6. ANS: A PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Using the SSS and SAS Postulates STA: CA GEOM 2.0| CA GEOM 5.0TOP: 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: 4-3.1 Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0| CA GEOM 5.0TOP: 4-3 Example 4 KEY: ASA | reasoning

8. ANS: C PTS: 1 DIF: L2 REF: 4-4 Using Congruent Triangles: CPCTC OBJ: 4-4.1 Proving Parts of Triangles Congruent STA: CA GEOM 5.0| CA GEOM 6.0TOP: 4-4 Example 1 KEY: ASA | CPCTC | proof

9. ANS: D PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 1KEY: segment bisector | isosceles triangle | proof

10. ANS: A PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 2KEY: angle bisector | isosceles triangle

ID: A

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11. ANS: B PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 3KEY: isosceles triangle | Isosceles Triangle Theorem | Polygon Angle-Sum Theorem

12. ANS: B PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 2KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem

13. ANS: A PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 2KEY: Isosceles Triangle Theorem | isosceles triangle

14. ANS: A PTS: 1 DIF: L1 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0 TOP: 4-5 Example 2KEY: Isosceles Triangle Theorem | isosceles triangle | problem solving | Triangle Angle-Sum Theorem

15. ANS: C PTS: 1 DIF: L2 REF: 4-6 Congruence in Right TrianglesOBJ: 4-6.1 The Hypotenuse-Leg Theorem STA: CA GEOM 2.0| CA GEOM 5.0TOP: 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: CPCTCOBJ: 4-4.1 Proving Parts of Triangles Congruent STA: CA GEOM 5.0| CA GEOM 6.0TOP: 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: CPCTCOBJ: 4-4.1 Proving Parts of Triangles Congruent STA: CA GEOM 5.0| CA GEOM 6.0TOP: 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 SASOBJ: 4-2.1 Using the SSS and SAS Postulates STA: CA GEOM 2.0| CA GEOM 5.0KEY: SAS | proof | reasoning

ID: A

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ESSAY

19. ANS: [4] Statement Reason

1. BC DA 1. Given

2. 1 2 2. 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. Given7. 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 TrianglesOBJ: 4-7.2 Using Two Pairs of Congruent Triangles STA: CA GEOM 5.0TOP: 4-7 Example 3 KEY: AAS | CPCTC | corresponding parts | congruent figures | proof | rubric-based question | extended response

20. ANS: [4]

Statement Reason1. BC EC and AC DC 1. Given2. BCA ECD 2. Vertical angles are congruent.3. BCA ECD 3. SAS4. 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: CPCTCOBJ: 4-4.1 Proving Parts of Triangles Congruent STA: CA GEOM 5.0| CA GEOM 6.0KEY: CPCTC | congruent figures | proof | SAS | rubric-based question | extended response