Geometry: Chapter 3 Ch. 3.3: Use Parallel Lines and Transversals.
Geometry Chapter 3 & 4...
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Name: ________________________ Class: ___________________ Date: __________ ID: B 1 Geometry Chapter 3 & 4 Test Use the diagram to find the following. ____ 1. What are three pairs of corresponding angles? A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4 B. angles 1 & 7, 2 & 4, and 6 & 7 D. angles 3 & 4, 7 & 8, and 1 & 6 ____ 2. Find the value of x. The diagram is not to scale. A. x = 13 B. x = 23 C. x = 40 D. none of these
Transcript of Geometry Chapter 3 & 4...
Name: ________________________ Class: ___________________ Date: __________ ID: B
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Geometry Chapter 3 & 4 Test
Use the diagram to find the following.
____ 1. What are three pairs of corresponding angles?
A. angles 1 & 2, 3 & 8, and 4 & 7 C. angles 1 & 7, 8 & 6, and 2 & 4
B. angles 1 & 7, 2 & 4, and 6 & 7 D. angles 3 & 4, 7 & 8, and 1 & 6
____ 2. Find the value of x. The diagram is not to scale.
A. x = 13 B. x = 23 C. x = 40 D. none of these
Name: ________________________ ID: B
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____ 3. What is the graph of y − (−2) = 1 / 3(x − (−3))?
A. C.
B. D.
____ 4. Find the value of x. The diagram is not to scale.
Given: ∠SRT ≅ ∠STR, m∠SRT = 34, m∠STU = 2x
A. 17 B. 73 C. 34 D. 36
Name: ________________________ ID: B
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____ 5. What is the missing reason in the two-column proof?
Given: QS→
bisects ∠TQR and SQ→
bisects ∠TSR
Prove: ∆TQS ≅ ∆RQS
Statements Reasons
1. QS→
bisects ∠TQR 1. Given
2. ∠TQS ≅ ∠RQS 2. Definition of angle bisector
3. QS ≅ QS 3. Reflexive property
4. SQ→
bisects ∠TSR 4. Given
5. ∠TSQ ≅ ∠RSQ 5. Definition of angle bisector
6. ∆TQS ≅ ∆RQS 6. ?
A. AAS Theorem C. SAS Postulate
B. SSS Postulate D. ASA Postulate
____ 6. Find the values of x and y. The diagram is not to scale.
A. x = 75, y = 63 C. x = 75, y = 65
B. x = 41, y = 63 D. x = 63, y = 75
____ 7. Find the value of x. The diagram is not to scale.
A. 42 B. 26 C. 16 D. 64
Name: ________________________ ID: B
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____ 8. What four segments are perpendicular to plane KLMJ?
A. segments PQ, QR, NR, and NP C. segments MR, LQ, KP, and JN
B. segments MR, LQ, NR and PQ D. segments NP, RQ, KP, and JN
____ 9. What four segments are parallel to plane PNRQ?
A. segments JN, MR, LQ, and KP C. segments JK, KL, ML, and JM
B. segments KP, LQ, JK, and ML D. segments NP, RQ, PQ, and JM
____ 10. Find the value of x. l � m. The diagram is not to scale.
A. 100 B. 140 C. 80 D. 40
____ 11. What is the value of x?
A. 59.25° B. 120.75° C. 61.5° D. 30.75°
Name: ________________________ ID: B
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____ 12. Supply the reasons missing from the proof shown below.
Given: AB ≅ AC, ∠BAD ≅ ∠CAD
Prove: 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. Definition of segment bisector
A. ASA; Corresp. parts of ≅ ∆ are ≅. C. SAS; Corresp. parts of ≅ ∆ are ≅.
B. SAS; Reflexive Property D. SSS; Reflexive Property
____ 13. What is an equation in point-slope form for the line perpendicular to y = 4x + 7 that contains (8, 1)?
A. y – 1 = 4(x – 8) C. y – 8 = −1
4(x – 1)
B. y – 1 = −1
4(x – 8) D. x – 1 = 4(y – 8)
Name: ________________________ ID: B
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____ 14. Justify the last two steps of the proof.
Given: RS ≅ UT and RT ≅ US
Prove: ∆RST ≅ ∆UTS
Proof:
1. RS ≅ UT 1. Given
2. RT ≅ US 2. Given
3. ST ≅ TS 3. ?
4. ∆RST ≅ ∆UTS 4. ?
A. Reflexive Property of ≅; SAS C. Symmetric Property of ≅; SSS
B. Reflexive Property of ≅; SSS D. Symmetric Property of ≅; SAS
____ 15. Find the value of x for which p is parallel to q, if m∠1 = (4x) and m∠3 = 112.The diagram is not to scale.
A. 108 B. 28 C. 112 D. 116
____ 16. Line r is parallel to line t. Find m∠6. The diagram is not to scale.
A. 143 B. 33 C. 137 D. 43
Name: ________________________ ID: B
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____ 17. Which two triangles are congruent by ASA?
MR bisects QO, and ∠MQP ≅ ∠ROP.
A. ∆MNP and ∆ONP C. ∆MQP and ∆MPN
B. ∆MPQ and ∆RPO D. none
____ 18. What common side do ∆AEG and ∆ADE share?
A. DG C. AE
B. AD D. EG
____ 19. Find the value of x. The diagram is not to scale.
Given: RS ≅ ST , m∠RST = 6x − 60, m∠STU = 7x
A. 150 B. 17 C. 15 D. 20
Name: ________________________ ID: B
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____ 20. Two sides of an equilateral triangle have lengths 2x + 4 and −3x + 34. Which could be the length of the third
side: 22 − x or 6x − 6?
A. 22 – x only C. both 22 – x and 6x – 6
B. 6x – 6 only D. neither 22 – x nor 6x – 6
____ 21. What is the slope of the line shown?
A.3
5C.
5
3
B. −5
3D. −
3
5
____ 22. Find the values of x and y.
A. x = 90, y = 42 C. x = 42, y = 48
B. x = 48, y = 42 D. x = 90, y = 48
Name: ________________________ ID: B
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____ 23. What is the slope of the line shown?
A. −7
9C.
9
7
B.7
9D. −
9
7
____ 24. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
A. AB ⊥ AD C. ∠CBA ≅ ∠CDA
B. ∠BAC ≅ ∠DAC D. AB ≅ AD
____ 25. Find m∠Q. The diagram is not to scale.
A. 71 B. 109 C. 81 D. 112
Name: ________________________ ID: B
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____ 26. Each sheet of metal on a roof is perpendicular to the top line of the roof. What can you
conclude about the relationship between the sheets of roofing? Justify your answer.
A. The sheets of metal are all parallel to each other by the Transitive Property of Parallel
Lines.
B. The sheets of metal are all parallel to each other because in a plane, if two lines
are perpendicular to the same line, then they are parallel to each other.
C. The sheets of metal are all parallel to each other because in a plane, if a line
is perpendicular to one of two parallel lines, then it is also perpendicular to the other.
D. The sheets of metal are all parallel to each other by the Alternate Interior Angles
Theorem.
____ 27. The expressions in the figure below represent the measures of two angles. Find the value of x. f � g . The
diagram is not to scale.
A. 19 B. 20 C. 21 D. –20
Name: ________________________ ID: B
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____ 28. What is the relationship between ∠3 and ∠5?
A. alternate interior angles C. corresponding angles
B. alternate exterior angles D. same-side interior angles
____ 29. BE→
is the bisector of ∠ABC and CD→
is the bisector of ∠ACB. Also, ∠XBA ≅ ∠YCA. Which of AAS, SSS,
SAS, or ASA would you use to help you prove BL ≅ CM ?
A. SAS B. AAS C. SSS D. ASA
____ 30. Write the equation for the horizontal line that contains point G(–9, 6).
A. x = –9 B. y = 6 C. y = –9 D. x = 6
____ 31. The folding chair has different settings that change the angles formed by its parts. Suppose m∠2 is 30 and
m∠3 is 81. Find m∠1. The diagram is not to scale.
A. 121 B. 101 C. 131 D. 111
Name: ________________________ ID: B
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____ 32. What is an equation in slope-intercept form for the line given?
A. y = −9 / 5(x) − (2) C. y = −9 / 5(x) + (−7 / 5)
B. y = −5 / 9(x) + (−7 / 5) D. y = −5 / 9(x) + (−43 / 5)
ID: B
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Geometry Chapter 3 & 4 Test
Answer Section
1. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles
OBJ: 3-1.2 To identify angles formed by two lines and a transversal
NAT: CC G.CO.1| CC G.CO.12| M.1.d| G.3.g STA: 4.1.PO 4
TOP: 3-1 Problem 2 Identifying an Angle Pair
KEY: corresponding angles | transversal | parallel lines
2. ANS: B PTS: 1 DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 3 Finding Angle Measures
KEY: Isosceles Triangle Theorem | isosceles triangle
3. ANS: B PTS: 1 DIF: L4
REF: 3-7 Equations of Lines in the Coordinate Plane
OBJ: 3-7.1 To graph and write linear equations NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 3| 4.3.PO 4| 4.3.PO 5 TOP: 3-7 Problem 2 Graphing Lines
KEY: graphing | slope-intercept form | slope | y-intercept
4. ANS: B PTS: 1 DIF: L4 REF: 3-5 Parallel Lines and Triangles
OBJ: 3-5.2 To find measures of angles of triangles NAT: CC G.CO.10| M.1.d| G.3.g
STA: 4.1.PO 4 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem
KEY: exterior angle of a polygon | remote interior angles
5. ANS: D PTS: 1 DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: 4.1.PO 8| 5.2.PO 12
TOP: 4-3 Problem 2 Writing a Proof Using ASA KEY: ASA | proof | two-column proof
6. ANS: A PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
NAT: CC G.CO.9| M.1.d| G.3.g STA: 4.1.PO 4| 5.2.PO 12
TOP: 3-2 Problem 4 Finding an Angle Measure KEY: corresponding angles | parallel lines
7. ANS: C PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles
OBJ: 3-5.2 To find measures of angles of triangles NAT: CC G.CO.10| M.1.d| G.3.g
STA: 4.1.PO 4 TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem
KEY: triangle | sum of angles of a triangle | vertical angles
8. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles
OBJ: 3-1.1 To identify relationships between figures in space
NAT: CC G.CO.1| CC G.CO.12| M.1.d| G.3.g STA: 4.1.PO 4
TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes
KEY: parallel planes | parallel lines
9. ANS: C PTS: 1 DIF: L3 REF: 3-1 Lines and Angles
OBJ: 3-1.1 To identify relationships between figures in space
NAT: CC G.CO.1| CC G.CO.12| M.1.d| G.3.g STA: 4.1.PO 4
TOP: 3-1 Problem 1 Identifying Nonintersecting Lines and Planes
KEY: parallel planes | parallel lines
ID: B
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10. ANS: D PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
NAT: CC G.CO.9| M.1.d| G.3.g STA: 4.1.PO 4| 5.2.PO 12
TOP: 3-2 Problem 4 Finding an Angle Measure
KEY: corresponding angles | parallel lines | angle pairs
11. ANS: D PTS: 1 DIF: L3
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra
KEY: Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | isosceles triangle
12. ANS: C PTS: 1 DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 1 Using the Isosceles Triangle Theorems
KEY: segment bisector | isosceles triangle | proof | two-column proof
13. ANS: B PTS: 1 DIF: L3
REF: 3-8 Slopes of Parallel and Perpendicular Lines
OBJ: 3-8.1 To relate slope to parallel and perpendicular lines NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 4| 4.1.PO 4| 4.3.PO 4 TOP: 3-8 Problem 4 Writing Equations of Perpendicular Lines
KEY: slopes of perpendicular lines | perpendicular lines
14. ANS: B PTS: 1 DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: 4.1.PO 8 TOP: 4-2 Problem 1 Using SSS
KEY: SSS | reflexive property | proof
15. ANS: B PTS: 1 DIF: L4 REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 To determine whether two lines are parallel NAT: CC G.CO.9| G.3.b| G.3.g
STA: 4.1.PO 4| 5.2.PO 12 TOP: 3-3 Problem 4 Using Algebra
KEY: parallel lines | angle pairs
16. ANS: D PTS: 1 DIF: L3 REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
NAT: CC G.CO.9| M.1.d| G.3.g STA: 4.1.PO 4| 5.2.PO 12
TOP: 3-2 Problem 1 Identifying Supplementary Angles
KEY: parallel lines | alternate interior angles
17. ANS: B PTS: 1 DIF: L4
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 To prove two triangles congruent using the ASA Postulate and the AAS theorem
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: 4.1.PO 8| 5.2.PO 12
TOP: 4-3 Problem 1 Using ASA KEY: ASA | vertical angles
18. ANS: C PTS: 1 DIF: L3
REF: 4-7 Congruence in Overlapping Triangles
OBJ: 4-7.1 To identify congruent overlapping triangles NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e
STA: 4.1.PO 8 TOP: 4-7 Problem 1 Identifying Common Parts
KEY: overlapping triangle | congruent parts
ID: B
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19. ANS: C PTS: 1 DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra
KEY: Isosceles Triangle Theorem | isosceles triangle | problem solving | Triangle Angle-Sum Theorem
20. ANS: A PTS: 1 DIF: L4
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra
KEY: equilateral triangle | word problem | problem solving
21. ANS: D PTS: 1 DIF: L3
REF: 3-7 Equations of Lines in the Coordinate Plane
OBJ: 3-7.1 To graph and write linear equations NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 3| 4.3.PO 4| 4.3.PO 5 TOP: 3-7 Problem 1 Finding Slopes of Lines
KEY: slope | linear graph | graph of line
22. ANS: A PTS: 1 DIF: L3
REF: 4-5 Isosceles and Equilateral Triangles
OBJ: 4-5.1 To use and apply properties of isosceles and equilateral triangles
NAT: CC G.CO.10| CC G.CO.13| CC G.SRT.5| G.1.c| G.2.e| G.3.e
STA: 4.1.PO 8 TOP: 4-5 Problem 2 Using Algebra KEY: angle bisector | isosceles triangle
23. ANS: C PTS: 1 DIF: L3
REF: 3-7 Equations of Lines in the Coordinate Plane
OBJ: 3-7.1 To graph and write linear equations NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 3| 4.3.PO 4| 4.3.PO 5 TOP: 3-7 Problem 1 Finding Slopes of Lines
KEY: slope | linear graph | graph of line
24. ANS: D PTS: 1 DIF: L4
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: 4.1.PO 8 TOP: 4-2 Problem 2 Using SAS
KEY: SAS | reasoning
25. ANS: A PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
NAT: CC G.CO.9| M.1.d| G.3.g STA: 4.1.PO 4| 5.2.PO 12
TOP: 3-2 Problem 3 Finding Measures of Angles KEY: angle | parallel lines | transversal
26. ANS: B PTS: 1 DIF: L3
REF: 3-4 Parallel and Perpendicular Lines
OBJ: 3-4.1 To relate parallel and perpendicular lines NAT: CC G.MG.3| G.3.b| G.3.g
STA: 4.1.PO 4| 5.2.PO 12 TOP: 3-4 Problem 1 Solving a Problem with Parallel Lines
KEY: parallel | perpendicular | transversal | word problem | reasoning
27. ANS: B PTS: 1 DIF: L4 REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
NAT: CC G.CO.9| M.1.d| G.3.g STA: 4.1.PO 4| 5.2.PO 12
TOP: 3-2 Problem 4 Finding an Angle Measure
KEY: corresponding angles | parallel lines | angle pairs
ID: B
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28. ANS: D PTS: 1 DIF: L3 REF: 3-1 Lines and Angles
OBJ: 3-1.2 To identify angles formed by two lines and a transversal
NAT: CC G.CO.1| CC G.CO.12| M.1.d| G.3.g STA: 4.1.PO 4
TOP: 3-1 Problem 3 Classifying an Angle Pair
KEY: angle pairs | transversal | parallel lines
29. ANS: D PTS: 1 DIF: L4
REF: 4-7 Congruence in Overlapping Triangles
OBJ: 4-7.2 To prove two triangles congruent using other congruent triangles
NAT: CC G.SRT.5| G.2.e| G.3.e| G.5.e STA: 4.1.PO 8 TOP: 4-7 Problem 2 Using Common Parts
KEY: corresponding parts | congruent figures | ASA | SAS | AAS | SSS | reasoning
30. ANS: B PTS: 1 DIF: L3
REF: 3-7 Equations of Lines in the Coordinate Plane
OBJ: 3-7.1 To graph and write linear equations NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 3| 4.3.PO 4| 4.3.PO 5
TOP: 3-7 Problem 5 Writing Equations of Horizontal and Vertical Lines
KEY: horizontal line
31. ANS: D PTS: 1 DIF: L3 REF: 3-5 Parallel Lines and Triangles
OBJ: 3-5.2 To find measures of angles of triangles NAT: CC G.CO.10| M.1.d| G.3.g
STA: 4.1.PO 4 TOP: 3-5 Problem 3 Applying the Triangle Theorems
KEY: triangle | sum of angles of a triangle | word problem | exterior angle of a polygon
32. ANS: C PTS: 1 DIF: L4
REF: 3-7 Equations of Lines in the Coordinate Plane
OBJ: 3-7.1 To graph and write linear equations NAT: CC G.GPE.5| G.3.g| G.4.a| G.4.d
STA: 3.3.PO 3| 4.3.PO 4| 4.3.PO 5 TOP: 3-7 Problem 4 Using Two Points to Write an Equation
KEY: point-slope form
