Download Geometry Chapter 5 Test

Name: ______________________
Class: _________________
Date: _________
Geometry Chapter 5 Test
Multiple Choice
Identify 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 ∠DCB
Prove: ΔDAC ≅ ΔBAC
Statements
Reasons
1. AC bisects ∠DAB
2. ∠DAC ≅ ∠BAC
3. AC ≅ AC
1. Given
2. Definition of angle bisector
3. Reflexive property
4. CA bisects ∠DCB
5. ∠DCA ≅ ∠BCA
6. ΔDAC ≅ ΔBAC
4. Given
5. Definition of angle bisector
6. ?
⎯⎯
→
⎯⎯
→
A. AAS Theorem
B. ASA Postulate
C. SAS Postulate
D. SSS Postulate
2. Use the information given in the diagram. Tell why AC ≅ AC and ∠BCA ≅ ∠DAC.
A.
B.
C.
D.
Reflexive Property, Given
Transitive Property, Reflexive Property
Given, Reflexive Property
Reflexive Property, Transitive Property
1
ID: A
Name: ______________________
ID: A
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
5. If BCDE is congruent to OPQR, then DE is congruent to
A. PQ
B. OR
D. 60
? .
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
B. AC ⊥ BD
C. ∠BAC ≅ ∠DAC
D. AC ≅ BD
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Name: ______________________
ID: A
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 ≅ US
Prove: ΔRST ≅ ΔUTS
Proof:
1. RS ≅ UT
2. RT ≅ US
3. ST ≅ TS
4. ΔRST ≅ ΔUTS
1. Given
2. Given
3. ?
4.
?
A. Symmetric Property of ≅; SSS
B. Symmetric Property of ≅; SAS
C. Reflexive Property of ≅; SSS
D. Reflexive Property of ≅; SAS
9. From the information in the diagram, can you prove ΔFDG ≅ ΔFDE? Explain.
A. yes, by ASA
B. yes, by SAS
C. yes, by AAA
D. no
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Name: ______________________
ID: A
10. What theorem or postulate allows you to prove the triangles congruent?
A. ASA
B. AAS
C. SAS
D. not possible
11. What else must you know to prove the triangles congruent by ASA?
A. ∠ADC ≅ ∠CAB;
B. ∠ACD ≅ ∠CAB;
C. ∠CAD ≅ ∠CBA;
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
B. ΔHIJ ≅ ΔLKJ by SAS
C. ΔHIJ ≅ ΔJLK by AAS
D. ΔHIJ ≅ ΔJLK by HL
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Name: ______________________
ID: A
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
B. ΔEFD ≅ ΔGHF
C. ΔFDE ≅ ΔFGH
D. ΔEDF ≅ ΔGFH
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Name: ______________________
ID: A
15. Supply the missing reasons to complete the proof.
Given: ∠Q ≅ ∠T and QR ≅ TR
Prove: PR ≅ SR
Statement
1. ∠Q ≅ ∠T and
Reasons
1. Given
QR ≅ TR
2. ∠PRQ ≅ ∠SRT
2. Vertical angles are congruent.
3. ΔPRQ ≅ ΔSRT
3.
?
4. PR ≅ SR
4.
?
A. AAS; CPCTC
B. ASA; Substitution
C. SAS; CPCTC
D. ASA; CPCTC
16. What additional information will allow you to prove the triangles congruent by the HL Theorem?
A. AC ≅ BD
B. ∠A ≅ ∠E
C. AC ≅ DC
D. m∠BCE = 90
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Name: ______________________
ID: A
17. Find AB.
A. AB = 20
B. AB = 10
C. AB = 54
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.
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Name: ______________________
ID: A
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 Response
Identify 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
B. The value of x is 14.
C. The value of y is −10.
D. ∠BEA ≅ ∠DEC
E.
CDE ≅ BAE
F.
EBA ≅ EDC
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Name: ______________________
ID: A
Short Answer
21. Find the measure of each acute angle.
Essay
22. Write a two-column proof.
Given: BC ≅ EC and AC ≅ DC
Prove: BA ≅ ED
23. Write a two-column proof:
Given: ∠BAC ≅ ∠DAC, ∠DCA ≅ ∠BCA
Prove: BC ≅ CD
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Name: ______________________
ID: A
Other
Write a proof.
24. Given ∠N ≅ ∠P, NO ≅ PL
Prove
NOM ≅ PLM
25. Given J is the midpoint of KM, JL⊥KM
Prove
JKL ≅ JML
10
ID: A
Geometry Chapter 5 Test
Answer Section
MULTIPLE CHOICE
1. ANS:
REF:
OBJ:
TOP:
2. ANS:
OBJ:
TOP:
3. ANS:
OBJ:
STA:
KEY:
4. ANS:
OBJ:
TOP:
5. ANS:
OBJ:
TOP:
6. ANS:
REF:
STA:
KEY:
7. ANS:
OBJ:
STA:
KEY:
8. ANS:
REF:
STA:
KEY:
9. ANS:
REF:
OBJ:
TOP:
10. ANS:
REF:
OBJ:
TOP:
11. ANS:
REF:
OBJ:
TOP:
B
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0| CA GEOM 5.0
4-3 Example 4
KEY: ASA | proof
A
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Congruent Figures
STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0
4-1 Example 4
KEY: congruent figures | corresponding parts | proof
A
PTS: 1
DIF: L2
REF: 4-5 Isosceles and Equilateral Triangles
4-5.1 The Isosceles Triangle Theorems
CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0
TOP: 4-5 Example 2
isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
D
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Congruent Figures
STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0
4-1 Example 1
KEY: congruent figures | corresponding parts
D
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Congruent Figures
STA: CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0
4-1 Example 1
KEY: congruent figures | corresponding parts | word problem
B
PTS: 1
DIF: L2
4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Using the SSS and SAS Postulates
CA GEOM 2.0| CA GEOM 5.0
TOP: 4-2 Example 2
SAS | reasoning
D
PTS: 1
DIF: L2
REF: 4-5 Isosceles and Equilateral Triangles
4-5.1 The Isosceles Triangle Theorems
CA GEOM 4.0| CA GEOM 5.0| CA GEOM 12.0
TOP: 4-5 Example 2
isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
C
PTS: 1
DIF: L2
4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Using the SSS and SAS Postulates
CA GEOM 2.0| CA GEOM 5.0
TOP: 4-2 Example 1
SSS | reflexive property | proof
A
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0| CA GEOM 5.0
4-3 Example 3
KEY: ASA | reasoning
B
PTS: 1
DIF: L3
4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0| CA GEOM 5.0
4-3 Example 3
KEY: ASA | AAS | reasoning
B
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem STA: CA GEOM 2.0| CA GEOM 5.0
4-3 Example 3
KEY: ASA | SAS | reasoning
1
ID: A
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 5.0
TOP: 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 5.0
TOP: 4-3 Example 3
KEY: ASA | AAS | SAS
14. ANS: C
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
OBJ: 4-1.1 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
15. ANS: D
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 6.0
TOP: 4-4 Example 1
KEY: ASA | CPCTC | proof
16. ANS: C
PTS: 1
DIF: L2
REF: 4-6 Congruence in Right Triangles
OBJ: 4-6.1 The Hypotenuse-Leg Theorem
STA: CA GEOM 2.0| CA GEOM 5.0
TOP: 4-6 Example 1
KEY: HL Theorem | right triangle | reasoning
17. ANS: C
PTS: 1
DIF: Level 1
REF: Geometry Sec. 6.1
NAT: HSG-CO.C.9 | HSG-MG.A.1
KEY: perpendicular bisector
NOT: 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 5.0
TOP: 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 5.0
KEY: ASA | AAS NOT: x = 9, y = 3
MULTIPLE RESPONSE
20. ANS:
NAT:
KEY:
NOT:
B, D, F
PTS: 1
DIF: Level 2
REF: Geometry Sec. 5.2
HSG-CO.B.7
Third Angles Theorem | corresponding parts | congruent figures
Combined Concept
SHORT ANSWER
21. ANS:
26°, 64°
PTS: 1
DIF: Level 1
NAT: HSG-CO.C.10
NOT: Example 4
REF: Geometry Sec. 5.1
KEY: interior angles
2
ID: A
ESSAY
22. ANS:
[4]
Statement
1.
2.
3.
4.
BC ≅ EC and AC ≅ DC
∠BCA ≅ ∠ECD
ΔBCA ≅ ΔECD
BA ≅ ED
Reason
1. Given
2. Vertical angles are congruent.
3. SAS
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: 4-4.1 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
23. ANS:
[4]
Statement
Reason
1. ∠BAC ≅ ∠DAC and
1. Given
∠DCA ≅ ∠BCA
2. Reflexive Property
2. CA ≅ CA
3. ΔCBA ≅ ΔCDA
3. ASA
4. CPCTC
4. BC ≅ CD
[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: 4-4.1 Proving Parts of Triangles Congruent
STA: CA GEOM 5.0| CA GEOM 6.0
KEY: ASA | CPCTC | congruent figures | corresponding parts | rubric-based question | extended response |
proof
3
ID: A
OTHER
24. ANS:
STATEMENTS
1. M is the midpoint of LO and
REASONS
1. Given
NP, NO ≅ PL
2. NM ≅ PM, LM ≅ OM
3. ∠N ≅ ∠P
2. Definition of midpoint
4. ∠NMO ≅ ∠PML
5. ∠O ≅ ∠L
6. NOM ≅ PLM
4. Vertical Angles Congruence Theorem
5. Third Angles Theorem
6. All corresponding parts are congruent.
PTS: 1
DIF: Level 1
NAT: HSG-CO.B.7
NOT: Example 5
25. ANS:
STATEMENTS
3. Given
REF: Geometry Sec. 5.2
KEY: congruent figures | congruent triangles
1. J is the midpoint of KM.
REASONS
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 Theorem
6. Reflexive Property of Congruence
6. LJ ≅ LJ
7. JKL ≅
JML
PTS: 1
DIF: Level 1
NAT: HSG-CO.B.8 | HSG-MG.A.1
NOT: Example 1
7. SAS Congruence Theorem
REF: Geometry Sec. 5.3
KEY: congruent triangles | SAS Congruence Theorem
4