geometry - chp 5 test review...in a right triangle, the measure of one acute angle is 11 times the...
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Name: _____________________________________________ Period: _______ Date: _________________
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Geometry - Chp 5 Test Review
____ 1. Classify the indicated triangular shape of the stained glass window in the diagram by its sides and by measuring its angles.
a. scalene acute c. isosceles obtuse b. equilateral equiangular d. isosceles acute
____ 2. Classify PQR by its sides. Then determine whether it is a right triangle.
a. isoceles ; right c. isoceles ; not rightb. scalene ; not right d. scalene ; right
Geometry - Chp 5 Test Review
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____ 3. Find m∠KMN.
a. 54° c. 9°b. 78° d. 102°
____ 4. In a right triangle, the measure of one acute angle is 11 times the sum of the measure of the other acute angle and 6. Find the measure of each acute angle.a. 13°, 77° c. 1°, 79°b. 1°, 89° d. 2°, 88°
____ 5. A ramp is designed with the profile of a right triangle. The measure of one acute angle is 5 times the measure of the other acute angle. Find the measure of each acute angle.
a. 4.5°, 85.5° c. 15°, 75°b. 18°, 72° d. 9°, 81°
Geometry - Chp 5 Test Review
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____ 6. Write a congruence statement for the triangles.
a. DEC≅ QOP c. DEC≅ OPQb. EDC≅ QOP d. EDC≅ OPQ
____ 7. In the diagram, CDE ≅ GHI. Find the value of y.
a. y = 43 c. y = 46b. y = 67 d. y = 55
Geometry - Chp 5 Test Review
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____ 8. Find m∠M.
a. 54° c. 63° b. 36° d. 27°
____ 9. Find m∠BDC.
a. 79° c. 101°b. 72° d. 58°
Geometry - Chp 5 Test Review
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____ 10. Find the value of x.
a. 60 c. 12b. 6 3 d. 6
____ 11. Find the value of x.
a. 4 c. 8b. 1 d. 7
Geometry - Chp 5 Test Review
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____ 12. In the diagram, M is the midpoint of BC. Find the coordinates of M.
a. 32
, 23
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃ c. 1, 3
2
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
b. 32
,1Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃ d. 2
3, 3
2
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
____ 13. Which statements about the diagram are true?
a. ABC is scalene. d. ABC is obtuse.b. The value of x is 30. e. The value of y is 123.c. BDE is obtuse. f. BDE is right.
Geometry - Chp 5 Test Review
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____ 14. In the diagram, point E is the midpoint of segments CA and BD. Which statements about the diagram are true?
a. ABE ≅ CDE d. ∠CDE ≅ ∠BAEb. ∠CDE ≅ ∠ABE e. CDE ≅ BAEc. The value of y is −4. f. The value of x is 25.
____ 15. What additional information is needed to prove that ABN ≅ DCN using the SAS Congruence Theorem?
a. ∠BND ≅ ∠CNA and CN ≅ BN c. ∠ABN ≅ ∠DCN and CN ≅ BNb. AN ≅ DN and ∠BAN ≅ ∠CDN d. AN ≅ DN and ∠ABN ≅ ∠DCN
____ 16. DEF and GEF have side EF in common. What additional information is needed to prove that DEF ≅ GEF?
a. DE ≅ GE and FD ≅ FG c. EF ⊥ DG and DE ≅ GEb. ∠EDF ≅ ∠EGF and DE ≅ GE d. DE ≅ GE and ∠FDE ≅ ∠FGE
Geometry - Chp 5 Test Review
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____ 17. In the diagram, ABD is equiangular. What additional information is needed to prove that ADC ≅ BDE?
a. ∠ADC ≅ ∠BDE and AC ≅ BE c. ∠DCA ≅ ∠DEB and ∠DAC ≅ ∠DBEb. ∠DAC ≅ ∠DBE and ∠ADC ≅ ∠BDE d. ∠DCA ≅ ∠DEB and AC ≅ BE
____ 18. Which statements about the diagram are true?
a. ∠ADC ≅ ∠CHJ c. ∠ADC ≅ ∠DACb. DH ≅ BH d. AF ≅ DH
____ 19. In a coordinate plane, PQR has vertices P(0, 0) and Q(a, 0). Which coordinates of vertex R make PQR an isosceles right triangle? Assume all variables are positive.
a. 0, aÊËÁÁ
ˆ¯̃̃ d. a, aÊ
ËÁÁˆ¯̃̃
b. a, a 32
Ê
Ë
ÁÁÁÁÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃˜̃̃˜
e. a 22
, a 22
Ê
Ë
ÁÁÁÁÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃˜̃̃˜
c. a2
, a2
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
Geometry - Chp 5 Test Review
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Write a proof.
20. Given J is the midpoint of KM,JL⊥KMProve JKL ≅ JML
21. Given AD ≅ CD,AB ≅ CBProve ADB ≅ CDB
22. Given AC ≅ DB,∠B and ∠C are right angles. Prove ABD ≅ DCA
Geometry - Chp 5 Test Review
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23. Given B is the midpoint of AE, AC Ä DEProve ABC ≅ EBD
24. Given T is the midpoint of SU, ∠SRT ≅ ∠UVTProve RST ≅ VUT
ID: A
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Geometry - Chp 5 Test ReviewAnswer Section
1. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.1NAT: HSG-MG.A.1 KEY: application | classifying trianglesNOT: Example 1
2. ANS: A PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.1NAT: HSG-MG.A.1 KEY: classifying triangles NOT: Example 2
3. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.1NAT: HSG-CO.C.10 KEY: exterior angles NOT: Example 3
4. ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.1NAT: HSG-CO.C.10 KEY: interior angles NOT: Example 4
5. ANS: C PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.1NAT: HSG-CO.C.10 KEY: application | interior anglesNOT: Example 4
6. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.2NAT: HSG-CO.B.7 KEY: corresponding parts NOT: Example 1
7. ANS: A PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.2NAT: HSG-CO.B.7 KEY: application | congruent figuresNOT: Example 2
8. ANS: B PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.2NAT: HSG-CO.B.7 KEY: Third Angles TheoremNOT: Example 4
9. ANS: C PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.2NAT: HSG-CO.B.7 KEY: Third Angles TheoremNOT: Example 4
10. ANS: D PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.4NAT: HSG-CO.C.10 | HSG-MG.A.1 KEY: application | finding measures in a triangleNOT: Example 2
11. ANS: B PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.4NAT: HSG-CO.C.10 | HSG-MG.A.1 KEY: application | finding measures in a triangleNOT: Example 3
12. ANS: B PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.8NAT: HSG-GPE.B.4 KEY: coordinate proof NOT: Example 5
13. ANS: A, B, D, F PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.1NAT: HSG-CO.C.10 | HSG-MG.A.1 KEY: classifying triangles | interior angles | exterior anglesNOT: Combined Concept
14. ANS: A, B, 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
ID: A
2
15. ANS: B, C PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.3NAT: HSG-CO.B.8 | HSG-MG.A.1 KEY: congruent triangles | SAS Congruence TheoremNOT: Combined Concept
16. ANS: A, C PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.5NAT: HSG-CO.B.8 | HSG-MG.A.1 | HSG-MG.A.3 KEY: congruent triangles | SSS Congruence Theorem | HL Congruence TheoremNOT: Combined Concept
17. ANS: B, C PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.6NAT: HSG-CO.B.8 KEY: congruent triangles | ASA Congruence Theorem | AAS Congruence TheoremNOT: Combined Concept
18. ANS: C, D PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.7NAT: HSG-SRT.B.5 KEY: congruent triangles NOT: Combined Concept
19. ANS: A, C, D PTS: 1 DIF: Level 2 REF: Geometry Sec. 5.8NAT: HSG-GPE.B.4 KEY: coordinate proof NOT: Combined Concept
20. 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
21. ANS: STATEMENTS REASONS1. AD ≅ CD 1. Given
2. AB ≅ CB 2. Given
3. DB ≅ DB 3. Reflexive Property of Congruence4. ADB ≅ CDB 4. SSS Congruence Theorem
PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.5 NAT: HSG-CO.B.8 | HSG-MG.A.1 KEY: congruent triangles | SSS Congruence TheoremNOT: Example 1
ID: A
3
22. ANS: STATEMENTS REASONS1. AC ≅ DB 1. Given
2. ∠B and ∠C are right angles. 2. Given
3. ABD and DCA are right triangles. 3. Definition of right triangle
4. AD ≅ DA 4. Reflexive Property of Congruence5. ABD ≅ DCA 5. HL Congruence Theorem
PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.5 NAT: HSG-CO.B.8 | HSG-MG.A.1 KEY: congruent triangles | HL Congruence TheoremNOT: Example 3
23. ANS: STATEMENTS REASONS1. B is the midpoint of AE. 1. Given
2. AC Ä DE 2. Given
3. AB ≅ EB 3. Definition of midpoint4. ∠ABC ≅ ∠DBE 4. Vertical Angles Congruence Theorem5. ∠CAB ≅ ∠DEB 5. Alternate Interior Angles Theorem6. ABC ≅ EBD 6. ASA Congruence Theorem
PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.6 NAT: HSG-CO.B.8 KEY: congruent triangles | ASA Congruence TheoremNOT: Example 2
24. ANS: STATEMENTS REASONS1. T is the midpoint of SU, ∠SRT ≅ ∠UVT 1. Given
2. ST ≅ UT 2. Definition of midpoint3. ∠STR ≅ ∠UTV 3. Vertical Angles Congruence Theorem4. RST ≅ VUT 4. AAS Congruence Theorem
PTS: 1 DIF: Level 1 REF: Geometry Sec. 5.6 NAT: HSG-CO.B.8 KEY: congruent triangles | AAS Congruence TheoremNOT: Example 3