Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry Chapter 5 Test

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

1. What is the missing reason in the two-column proof?Given: AC

→⎯⎯

bisects ∠DAB and CA→⎯⎯

bisects ∠DCBProve: ΔDAC ≅ ΔBAC

Statements Reasons1. AC

→⎯⎯

bisects ∠DAB 1. Given2. ∠DAC ≅ ∠BAC 2. Definition of angle bisector3. AC ≅ AC 3. Reflexive property

4. CA→⎯⎯

bisects ∠DCB 4. Given5. ∠DCA ≅ ∠BCA 5. Definition of angle bisector6. ΔDAC ≅ ΔBAC 6. ?

A. AAS Theorem C. SAS PostulateB. ASA Postulate D. SSS Postulate

2. Use the information given in the diagram. Tell why AC ≅ AC and ∠BCA ≅ ∠DAC.

A. Reflexive Property, GivenB. Transitive Property, Reflexive PropertyC. Given, Reflexive PropertyD. Reflexive Property, Transitive Property

Name: ______________________ ID: A

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3. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 34° and the two congruent sides each measure 21 units?

A. 73° B. 78° C. 156° D. 146°

4. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to scale.

A. 17 B. 90 C. 30 D. 60

5. If BCDE is congruent to OPQR, then DE is congruent to ? .

A. PQ B. OR C. OP D. QR

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

A. ∠CBA ≅ ∠CDA C. ∠BAC ≅ ∠DACB. AC ⊥ BD D. AC ≅ BD

Name: ______________________ ID: A

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7. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 54°?A. 63° B. 108° C. 126° D. 72°

8. Justify the last two steps of the proof.Given: RS ≅ UT and RT ≅ USProve: ΔRST ≅ ΔUTS

Proof:1. RS ≅ UT 1. Given2. RT ≅ US 2. Given3. ST ≅ TS 3. ?

4. ΔRST ≅ ΔUTS 4. ?

A. Symmetric Property of ≅; SSS C. Reflexive Property of ≅; SSSB. Symmetric Property of ≅; SAS D. Reflexive Property of ≅; SAS

9. From the information in the diagram, can you prove ΔFDG ≅ ΔFDE? Explain.

A. yes, by ASA C. yes, by AAAB. yes, by SAS D. no

Name: ______________________ ID: A

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10. What theorem or postulate allows you to prove the triangles congruent?

A. ASA C. SASB. AAS D. not possible

11. What else must you know to prove the triangles congruent by ASA?

A. ∠ADC ≅ ∠CAB; C. ∠CAD ≅ ∠CBA; B. ∠ACD ≅ ∠CAB; D. ∠ACD ≅ ∠CBA;

12. Based on the given information, what can you conclude, and why?Given: ∠H ≅ ∠L, HJ ≅ JL

A. ΔHIJ ≅ ΔLKJ by ASA C. ΔHIJ ≅ ΔJLK by AASB. ΔHIJ ≅ ΔLKJ by SAS D. ΔHIJ ≅ ΔJLK by HL

Name: ______________________ ID: A

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13. Name the theorem or postulate that lets you immediately conclude ΔABD ≅ ΔCBD.

A. ASA B. SAS C. AAS D. none of these

14. Which congruence statement does NOT necessarily describe the triangles shown if ΔDEF ≅ ΔFGH?

A. ΔFED ≅ ΔHGF C. ΔFDE ≅ ΔFGHB. ΔEFD ≅ ΔGHF D. ΔEDF ≅ ΔGFH

Name: ______________________ ID: A

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15. Supply the missing reasons to complete the proof.Given: ∠Q ≅ ∠T and QR ≅ TR

Prove: PR ≅ SR

Statement Reasons

1. ∠Q ≅ ∠T and

QR ≅ TR1. Given

2. ∠PRQ ≅ ∠SRT 2. Vertical angles are congruent.

3. ΔPRQ ≅ ΔSRT 3. ?

4. PR ≅ SR 4. ?

A. AAS; CPCTC C. SAS; CPCTCB. ASA; Substitution D. ASA; CPCTC

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

A. AC ≅ BD C. AC ≅ DCB. ∠A ≅ ∠E D. m∠BCE = 90

Name: ______________________ ID: A

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17. Find AB.

A. AB = 20 C. AB = 54B. AB = 10 D. AB = 12

18. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?A. C.

B. D.

Name: ______________________ ID: A

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19. Free Response

ΔABC ≅ ΔDEF. AB = 3y, ED = x, AC = 16 - y and DF = x + 4. Solve for x and y.

A. x = B. y =

Multiple ResponseIdentify one or more choices that best complete the statement or answer the question.

20. In the diagram, point E is the midpoint of segments CA and BD. Which statements about the diagram are true?

A. ∠BEA ≅ ∠DCE D. ∠BEA ≅ ∠DEC B. The value of x is 14. E. CDE ≅ BAEC. The value of y is −10. F. EBA ≅ EDC

Name: ______________________ ID: A

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Short Answer

21. Find the measure of each acute angle.

Essay

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

23. Write a two-column proof:Given: ∠BAC ≅ ∠DAC, ∠DCA ≅ ∠BCAProve: BC ≅ CD

Name: ______________________ ID: A

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Other

Write a proof.

24. Given ∠N ≅ ∠P,NO ≅ PLProve NOM ≅ PLM

25. Given J is the midpoint of KM,JL⊥KMProve JKL ≅ JML

ID: A

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Geometry Chapter 5 TestAnswer Section

MULTIPLE CHOICE

1. ANS: B 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 | proof

2. 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 4 KEY: congruent figures | corresponding parts | proof

3. ANS: A PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 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

4. 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

5. 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

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

7. ANS: D PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 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 | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem

8. ANS: C PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Using the SSS and SAS PostulatesSTA: CA GEOM 2.0| CA GEOM 5.0 TOP: 4-2 Example 1 KEY: SSS | reflexive property | proof

9. ANS: A 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 3 KEY: ASA | reasoning

10. ANS: B PTS: 1 DIF: L3 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 3 KEY: ASA | AAS | reasoning

11. ANS: B 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 3 KEY: ASA | SAS | reasoning

ID: A

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12. ANS: A 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

13. ANS: B 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 3 KEY: ASA | AAS | SAS

14. ANS: C 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

15. ANS: D 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 1 KEY: ASA | CPCTC | proof

16. 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

17. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 6.1NAT: HSG-CO.C.9 | HSG-MG.A.1 KEY: perpendicular bisectorNOT: Example 1

18. 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 1 KEY: ASA

19. ANS: A PTS: 1 DIF: L3 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 5.0KEY: ASA | AAS NOT: x = 9, y = 3

MULTIPLE RESPONSE

20. ANS: B, D, F PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.2NAT: HSG-CO.B.7 KEY: Third Angles Theorem | corresponding parts | congruent figuresNOT: Combined Concept

SHORT ANSWER

21. ANS: 26°, 64°

PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.1 NAT: HSG-CO.C.10 KEY: interior angles NOT: Example 4

ID: A

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ESSAY

22. ANS: [4]

Statement Reason1. BC ≅ EC and AC ≅ DC 1. Given2. ∠BCA ≅ ∠ECD 2. Vertical angles are congruent.3. ΔBCA ≅ ΔECD 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

23. ANS: [4]

Statement Reason1. ∠BAC ≅ ∠DAC and ∠DCA ≅ ∠BCA 1. Given

2. CA ≅ CA 2. Reflexive Property3. ΔCBA ≅ ΔCDA 3. ASA4. BC ≅ CD 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: ASA | CPCTC | congruent figures | corresponding parts | rubric-based question | extended response | proof

ID: A

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OTHER

24. ANS: STATEMENTS REASONS1. M is the midpoint of LO and NP,NO ≅ PL

1. Given

2. NM ≅ PM,LM ≅ OM 2. Definition of midpoint3. ∠N ≅ ∠P 3. Given

4. ∠NMO ≅ ∠PML 4. Vertical Angles Congruence Theorem 5. ∠O ≅ ∠L 5. Third Angles Theorem6. NOM ≅ PLM 6. All corresponding parts are congruent.

PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.2 NAT: HSG-CO.B.7 KEY: congruent figures | congruent trianglesNOT: Example 5

25. ANS: STATEMENTS REASONS1. J is the midpoint of KM. 1. Given

2. KJ ≅ MJ 2. Definition of midpoint

3. JL⊥KM 3. Given

4. ∠LJMand ∠LJK are right angles. 4. Definition of perpendicular lines

5. ∠LJM ≅ ∠LJK 5. Right Angles Congruence Theorem6. LJ ≅ LJ 6. Reflexive Property of Congruence7. JKL ≅ JML 7. SAS Congruence Theorem

PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.3 NAT: HSG-CO.B.8 | HSG-MG.A.1 KEY: congruent triangles | SAS Congruence TheoremNOT: Example 1