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Unit 1 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. How are the two angles related?
52°
128°
Drawing not to scale
a. vertical
b. supplementary
____
2. Name an angle supplementary to
a.
____
b.
c.
d.
c.
d.
3. Name an angle complementary to
a.
____
c. complementary
d. adjacent
b.
4. Name an angle vertical to
E
D
F
G
H
J
I
a.
____
b.
c.
d.
c.
d.
5. Name an angle adjacent to
E
D
F
G
H
J
I
a.
b.
____
6. Supplementary angles are two angles whose measures have a sum of ____.
Complementary angles are two angles whose measures have a sum of ____.
a. 90; 180
b. 90; 45
c. 180; 360
d. 180; 90
____
7. Two angles whose sides are opposite rays are called ____ angles. Two coplanar angles with a common side, a
common vertex, and no common interior points are called ____ angles.
a. vertical; adjacent
b. adjacent; vertical
c. vertical; supplementary
d. adjacent; complementary
____
8. In the figure shown,
. Which of the following statements is false?
Not drawn to scale
a.
b.
c.
d.
____
BEC and
CED are adjacent angles.
AED and
BEC are adjacent angles.
9. What can you conclude from the information in the diagram?
P
U
S
Q
R
T
a. 1.
2.
3.
b. 1.
2.
3.
c. 1.
2.
3.
d. 1.
2.
3.
are vertical angles
are adjacent angles
is a right angle
are vertical angles
is a right angle
are adjacent angles
____ 10. The complement of an angle is 25°. What is the measure of the angle?
a. 75°
b. 155°
c. 65°
d. 165°
____ 11.
____ 12.
and
are complementary angles. m
each angle.
a.
= 47,
= 53
c.
b.
= 47,
= 43
d.
and
are a linear pair.
, and
=
, and m
= 52,
= 52,
=
. Find the measure of
= 48
= 38
. Find the measure of each angle.
a.
b.
c.
d.
____ 13. Angle A and angle B are a linear pair. If
a. 45, 135
b. 22.5, 67.5
____ 14.
bisects
, and
a. 6x – 9
____ 15.
, find
c. 67.5, 22.5
b. 6x – 18
c. 3x – 9
bisects
diagram is not to scale.
bisects
a. 61
d. 135, 45
. Write an expression for
. The diagram is not to scale.
d. 1.5x – 4.5
and
a. x = 13,
b. x = 13,
____ 16.
and
Solve for x and find
The
c. x = 14,
d. x = 14,
,
,
b. 45.75
. Find
c. 91.5
____ 17. What is the value of x? Identify the missing justifications.
,
, and
.
. The diagram is not to scale.
d. 66
P
R
Q
S
Drawing not to scale
x + 7 + x + 3 = 100
2x + 10 = 100
2x = 90
x = 45
a.
b.
c.
d.
____ 18.
a. __________
b. Substitution Property
c. Simplify
d. __________
e. Division Property of Equality
Angle Addition Postulate; Addition Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Protractor Postulate; Addition Property of Equality
Protractor Postulate; Subtraction Property of Equality
bisects
a. 50
= 7x.
b. 125
=
. Find
c. 75
d. 175
____ 19. Name the Property of Equality that justifies this statement:
If p = q, then
.
a. Reflexive Property
c. Symmetric Property
b. Multiplication Property
d. Subtraction Property
____ 20. Which statement is an example of the Addition Property of Equality?
a. If p = q then
c. If p = q then
.
b. If p = q then
d. p = q
.
Use the given property to complete the statement.
____ 21. Transitive Property of Congruence
If
______.
a.
b.
c.
d.
____ 22. Multiplication Property of Equality
If
, then ______.
a.
b.
c.
d.
____ 23. Substitution Property of Equality
If
, then ______.
a.
b.
c.
d.
____ 24. Name the Property of Congruence that justifies the statement:
.
If
a. Symmetric Property
b. Transitive Property
.
c. Reflexive Property
d. none of these
____ 25. Name the Property of Congruence that justifies this statement:
If
.
a. Transitive Property
c. Reflexive Property
b. Symmetric Property
d. none of these
____ 26. Complete the two-column proof.
Given:
Prove:
a. a. Given
b. Symmetric Property of Equality
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
b. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
c. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
d. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Addition Property of Equality
e. Symmetric Property of Equality
____ 27. Complete the two-column proof.
Given:
Prove:
a. a. Given
b. Addition Property of Equality
c. Division Property of Equality
b. a. Given
c. a. Given
b. Addition Property of Equality
c. Multiplication Property of Equality
d. a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
b. Subtraction Property of Equality
c. Division Property of Equality
____ 28. What is the value of x?
(7x – 8)°
(6x + 11)°
Drawing not to scale
a. –19
b. 125
c. 19
d. 55
c. 159
d. 43
c. 27
d. 153
____ 29. What is the value of x?
(3x – 10)º
149º
Drawing not to scale
a. 63
____ 30.
b. 53
Find
1
4
2
3
Drawing not to scale
a. 37
b. 143
____ 31. Find the values of x and y.
4y°
7x + 7°
112°
Drawing not to scale
a. x = 15, y = 17
b. x = 112, y = 68
c. x = 68, y = 112
d. x = 17, y = 15
K
L
M
J
Q
P
N
R
____ 32. What four segments are parallel to plane PNRQ?
a. segments JK, KL, ML, and JM
c. segments NP, RQ, PQ, and JM
b. segments JN, MR, LQ, and KP
d. segments KP, LQ, JK, and ML
____ 33. What four segments are perpendicular to plane JKPN?
a. segments ML, LQ, RQ, and MR
c. segments MR, LQ, NR, and PQ
b. segments JM, KL, PQ, and NR
d. segments ML, RQ, JM, and NR
Use the diagram to find the following.
h
a
1
2
8
b
3
7
4
6
5
____ 34. Identify a pair of alternate exterior angles.
a.
b.
c.
d.
____ 35. What are three pairs of corresponding angles?
a. angles 1 & 2, 3 & 8, and 4 & 7
c. angles 3 & 4, 7 & 8, and 1 & 6
b. angles 1 & 7, 8 & 6, and 2 & 4
d. angles 1 & 7, 2 & 4, and 6 & 7
____ 36. Which angles are corresponding angles?
a.
b.
____ 37. What is the relationship between
c.
d. none of these
and
?
1
2
m
3
4
5
6
n
7
8
a. corresponding angles
b. same-side interior angles
c. alternate interior angles
d. alternate exterior angles
____ 38. Which statement is true?
a.
b.
c.
d.
are alternate angles.
are alternate angles.
are same-side interior angles.
are same-side interior angles.
This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both
runways.
____ 39. How are
and
related?
a. corresponding angles
b. alternate interior angles
c. same-side interior angles
d. none of these
____ 40. If 8 measures 119, what is the sum of the measures of 1 and 4?
a. 122
b. 238
c. 119
d. 299
____ 41. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r
7
135°
1
3
t
4
a. 45
2
5
6
b. 35
____ 42. Which is a correct two-column proof?
Given:
Prove:
and
n
are supplementary.
p
d
l
b
c
h
j
a.
b.
k
m
c. 135
d. 145
c.
d. none of these
____ 43. Which is a correct two-column proof?
Given:
and
are supplementary.
Prove:
k
A
C D
E F
G H
a.
b.
B
j
l
c.
d. none of these
____ 44. Find
The diagram is not to scale.
Q
R
76°
38°
a. 76
b. 104
____ 45. Find
c. 66
d. 114
. The diagram is not to scale.
G
H
p
r
34°
a. 34
____ 46. Find
b. 110
The diagram is not to scale.
c. 104
d. 146
P
g
>
>
>>
>>
130°
j
h
k
a. 50
b. 60
c. 40
d. 130
____ 47. The expressions in the figure below represent the measures of two angles. Find the value of x.
diagram is not to scale.
f
5x
9 x + 26
a. 10
g
b. 11
____ 48. Find the value of x.
c. 12
. The diagram is not to scale.
2x
l
64°
a. 148
m
b. 116
c. 64
____ 49. Find the values of x and y. The diagram is not to scale.
(x – 5)°
d. –11
55°
(y + 8)°
61°
a. x = 55, y = 56
b. x = 66, y = 58
____ 50. Which lines are parallel if
c. x = 56, y = 66
d. x = 66, y = 56
? Justify your answer.
d. 32
. The
g
1
2
j
a.
b.
c.
d.
h
k
, by the Converse of the Same-Side Interior Angles Theorem
, by the Converse of the Alternate Interior Angles Theorem
, by the Converse of the Alternate Interior Angles Theorem
, by the Converse of the Same-Side Interior Angles Theorem
____ 51. Which lines are parallel if
1 2
3 4
5 6
7
8
r
s
l
a.
b.
c.
d.
? Justify your answer.
m
, by the Converse of the Same-Side Interior Angles Theorem
, by the Converse of the Alternate Interior Angles Theorem
, by the Converse of the Alternate Interior Angles Theorem
, by the Converse of the Same-Side Interior Angles Theorem
____ 52. Find the value of x for which p is parallel to q, if
3 4
5
p
.The diagram is not to scale.
1 2
6
q
a. 108
b. 116
c. 28
d. 112
____ 53. Find the value of x for which l is parallel to m. The diagram is not to scale.
28°
l
56°
x°
a. 28
m
b. 56
c. 84
d. 152
____ 54. Find the value of x for which l is parallel to m. The diagram is not to scale.
80°
( 3 x - 43 )º
a. 100
l
m
b. 80
c. 123
d. 41
____ 55. Each tie on the railroad tracks is perpendicular to both of the tracks. What is the relationship between the two
tracks? Justify your answer.
a.
b.
c.
d.
The two tracks are perpendicular by the definition of complementary angles.
The two tracks are parallel by the Same-Side Interior Angles Theorem.
The two tracks are perpendicular by the Perpendicular Transversal Theorem.
The two tracks are parallel by the Converse of the Perpendicular Transversal Theorem.
____ 56. 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 by the Alternate Interior Angles Theorem.
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 because in a plane, if two lines are
perpendicular to the same line, then they are parallel to each other.
____ 57. If
and
, what do you know about the relationship between lines a and b? Justify your conclusion
with a theorem or postulate.
b
1 2
3 4
a
5 6
7 8
c
a.
, by the Perpendicular Transversal Theorem
b.
, by the Perpendicular Transversal Theorem
c.
, by the Alternate Exterior Angles Theorem
d. not enough information
Short Answer
58. What is the value of x? Identify the missing justifications.
(2x)°
6(x – 3)°
Drawing not to scale
59. Solve for x. Justify each step.
60. What is the value of x? Justify each step.
2x
6x + 8
Drawing not to scale
61. Complete the paragraph proof.
Given:
are supplementary, and
are supplementary.
Prove:
By the definition of supplementary angles,
by _____ (c). Subtract
_____ (e).
_____ (a) and
from each side. You get
62. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
_____ (b). Then
_____ (d), or
63. State the missing reasons in this proof.
Given:
Prove:
q
1
3 4
5 6
7 8
2
p
r
64. The 8 rowers in the racing boat stroke so that the angles formed by their oars with the side of the boat all stay
equal. Explain why their oars on either side of the boat remain parallel.
65. The map given shows the relationship between three streets. Suppose that
Street and Elm Street parallel? Explain.
Are Maple
Maple Street
Riv er
Driv e
1
Elm Street
2
Essay
66. Complete the two-column proof.
Given:
Prove:
Drawing not to scale
67. Given:
Prove:
are complementary, and
are complementary.
68. Given:
are supplementary, and
Prove:
.
are supplementary.
1
2
3
69. Write a two-column proof.
Given:
Prove:
are supplementary.
1
2
3
l
4
5
6
7
8
m
70. Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line, then they
are parallel to each other.
Given:
Prove:
s
1
2
3
4
5
6
7
8
r
t
Other
71. Write a two-column proof.
Given:
Prove:
72. Give a convincing argument that the following statement is true.
If two angles are congruent and complementary, then the measure of each is 45.
73. Given
, what can you conclude about the lines l, m, and n? Explain.
n
1
l
2
l
m
74. A carpenter cut the top section of window frame with a 37º angle on each end. The side pieces each have a
50º angle cut at their top end, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to
scale.
37°
37°
50°
50°
75. In a plane, line k is parallel to line l and line k is parallel to line m. What can you conclude about the
relationship between lines l and m?
k
l
m
>
>>
>
>>
Unit 1 Review
Answer Section
MULTIPLE CHOICE
1. ANS:
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11. ANS:
OBJ:
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B
PTS: 1
DIF: L2
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
supplementary angles
DOK: DOK 1
B
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
supplementary angles
DOK: DOK 1
D
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
supplementary angles
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
vertical angles
DOK: DOK 1
B
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
vertical angles
DOK: DOK 1
D
PTS: 1
DIF: L2
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
supplementary angles | complementary angles
DOK: DOK 1
A
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
adjacent angles | vertical angles
DOK: DOK 1
D
PTS: 1
DIF: L4
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 1 Identifying Angle Pairs
adjacent angles | supplementary angles | vertical angles
DOK: DOK 2
A
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 2 Making Conclusions From a Diagram
vertical angles | supplementary angles | adjacent angles | right angle | congruent segments
DOK 1
C
PTS: 1
DIF: L2
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 3 Finding Missing Angle Measures
complementary angles
DOK: DOK 1
D
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 3 Finding Missing Angle Measures
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complementary angles
DOK: DOK 2
B
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 3 Finding Missing Angle Measures
supplementary angles| linear pair
DOK: DOK 2
D
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
TOP: 1-5 Problem 3 Finding Missing Angle Measures
linear pair | supplementary angles DOK: DOK 2
B
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
1-5 Problem 4 Using an Angle Bisector to Find Angle Measures
angle bisector
DOK: DOK 2
D
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
1-5 Problem 4 Using an Angle Bisector to Find Angle Measures
angle bisector
DOK: DOK 2
A
PTS: 1
DIF: L3
REF: 1-5 Exploring Angle Pairs
1-5.1 Identify special angle pairs and use their relationships to find angle measures
MA.912.G.4.2
1-5 Problem 4 Using an Angle Bisector to Find Angle Measures
angle bisector
DOK: DOK 2
B
PTS: 1
DIF: L3
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 1 Justifying Steps When Solving an Equation
Properties of Equality | Angle Addition Postulate | deductive reasoning
DOK 2
D
PTS: 1
DIF: L4
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 1 Justifying Steps When Solving an Equation
Properties of Congruence | Properties of Equality | deductive reasoning
DOK 3
D
PTS: 1
DIF: L2
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Equality
DOK: DOK 1
B
PTS: 1
DIF: L2
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Equality
DOK: DOK 1
C
PTS: 1
DIF: L3
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 2 Using Properties of Equality and Congruence
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Properties of Congruence
DOK: DOK 1
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PTS: 1
DIF: L3
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Equality
DOK: DOK 1
C
PTS: 1
DIF: L3
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Equality
DOK: DOK 1
A
PTS: 1
DIF: L2
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Congruence
DOK: DOK 1
A
PTS: 1
DIF: L2
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 2 Using Properties of Equality and Congruence
Properties of Congruence
DOK: DOK 1
B
PTS: 1
DIF: L3
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 3 Writing a Two-Column Proof
KEY:
DOK 3
B
PTS: 1
DIF: L2
2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA:
2-5 Problem 3 Writing a Two-Column Proof
KEY:
DOK 2
C
PTS: 1
DIF: L3
REF:
2-6.1 Prove and apply theorems about angles
MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
2-6 Problem 1 Using the Vertical Angles Theorem
vertical angles | Vertical Angles Theorem
DOK:
B
PTS: 1
DIF: L2
REF:
2-6.1 Prove and apply theorems about angles
MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
2-6 Problem 1 Using the Vertical Angles Theorem
vertical angles | Vertical Angles Theorem
DOK:
A
PTS: 1
DIF: L2
REF:
2-6.1 Prove and apply theorems about angles
MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
2-6 Problem 1 Using the Vertical Angles Theorem
Vertical Angles Theorem | vertical angles
DOK:
A
PTS: 1
DIF: L4
REF:
2-6.1 Prove and apply theorems about angles
MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
2-6 Problem 1 Using the Vertical Angles Theorem
MA.912.D.6.4| MA.912.G.8.5
MA.912.D.6.4| MA.912.G.8.5
MA.912.D.6.4| MA.912.G.8.5
MA.912.D.6.4| MA.912.G.8.5
MA.912.D.6.4| MA.912.G.8.5
Properties of Equality | proof
MA.912.D.6.4| MA.912.G.8.5
Properties of Equality | proof
2-6 Proving Angles Congruent
DOK 2
2-6 Proving Angles Congruent
DOK 2
2-6 Proving Angles Congruent
DOK 2
2-6 Proving Angles Congruent
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
KEY:
DOK:
ANS:
OBJ:
TOP:
KEY:
ANS:
OBJ:
TOP:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
STA:
KEY:
ANS:
OBJ:
TOP:
KEY:
DOK:
ANS:
OBJ:
TOP:
Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question
DOK 2
A
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.1 Identify relationships between figures in space
STA: MA.912.G.7.2
3-1 Problem 1 Identifying Nonintersecting Lines and Planes
parallel | planes
DOK: DOK 2
B
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.1 Identify relationships between figures in space
STA: MA.912.G.7.2
3-1 Problem 1 Identifying Nonintersecting Lines and Planes
parallel | planes
DOK: DOK 2
D
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 2 Identifying an Angle Pair
transversal | angle pair
DOK: DOK 1
B
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 2 Identifying an Angle Pair
angle pair | transversal
DOK: DOK 1
A
PTS: 1
DIF: L2
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 2 Identifying an Angle Pair
corresponding angles | transversal | parallel lines
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 3 Classifying an Angle Pair
angle pair | transversal
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 3 Classifying an Angle Pair
same-side interior angles | alternate interior angles
DOK: DOK 1
A
PTS: 1
DIF: L2
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
MA.912.G.7.2
TOP: 3-1 Problem 3 Classifying an Angle Pair
parallel lines | transversal | angle
DOK: DOK 1
B
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
3-2.2 Use properties of parallel lines to find angle measures
MA.912.G.1.3
TOP: 3-2 Problem 3 Finding Measures of Angles
parallel lines | transversal
DOK: DOK 2
C
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
3-2.2 Use properties of parallel lines to find angle measures
MA.912.G.1.3
TOP: 3-2 Problem 1 Identifying Congruent Angles
parallel lines | alternate interior angles
DOK: DOK 2
A
PTS: 1
DIF: L2
REF: 3-2 Properties of Parallel Lines
3-2.1 Prove theorems about parallel lines
STA: MA.912.G.1.3
3-2 Problem 2 Proving an Angle Relationship
proof | two-column proof | supplementary angles | parallel lines | reasoning
DOK 3
A
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
3-2.1 Prove theorems about parallel lines
STA: MA.912.G.1.3
3-2 Problem 2 Proving an Angle Relationship
KEY: parallel lines | reasoning | supplementary angles
DOK: DOK 3
44. ANS: C
PTS: 1
DIF: L4
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
STA: MA.912.G.1.3
TOP: 3-2 Problem 3 Finding Measures of Angles
KEY: angle | parallel lines | transversal
DOK: DOK 2
45. ANS: A
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
STA: MA.912.G.1.3
TOP: 3-2 Problem 3 Finding Measures of Angles
KEY: angle | parallel lines | transversal
DOK: DOK 2
46. ANS: A
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
STA: MA.912.G.1.3
TOP: 3-2 Problem 3 Finding Measures of Angles
KEY: angle | parallel lines | transversal
DOK: DOK 2
47. ANS: B
PTS: 1
DIF: L4
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
STA: MA.912.G.1.3
TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure
KEY: corresponding angles | parallel lines | angle pairs
DOK: DOK 2
48. ANS: D
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
NAT: M.1.d| G.3.g TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure
KEY: corresponding angles | parallel lines | angle pairs
DOK: DOK 2
49. ANS: D
PTS: 1
DIF: L4
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 Use properties of parallel lines to find angle measures
STA: MA.912.G.1.3
TOP: 3-2 Problem 4 Using Algebra to Find an Angle Measure | 3-1 Problem 1 Identifying Nonintersecting
Lines and Planes
KEY: corresponding angles | parallel lines
DOK: DOK 2
50. ANS: A
PTS: 1
DIF: L2
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 1 Identifying Parallel Lines
KEY: parallel lines | reasoning
DOK: DOK 2
51. ANS: B
PTS: 1
DIF: L2
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 1 Identifying Parallel Lines
KEY: parallel lines | reasoning
DOK: DOK 2
52. ANS: C
PTS: 1
DIF: L4
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 4 Using Algebra
KEY: parallel lines | angle pairs
DOK: DOK 2
53. ANS: A
PTS: 1
DIF: L4
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 4 Using Algebra
KEY: parallel lines | transversal
DOK: DOK 2
54. ANS: D
PTS: 1
DIF: L3
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 4 Using Algebra
KEY: parallel lines | transversal
DOK: DOK 2
55. ANS: D
PTS: 1
DIF: L2
REF: 3-4 Parallel and Perpendicular Lines
OBJ: 3-4.1 Relate parallel and perpendicular lines STA:
MA.912.G.1.3
TOP:
KEY:
DOK:
56. ANS:
REF:
OBJ:
TOP:
KEY:
DOK:
57. ANS:
REF:
OBJ:
TOP:
KEY:
3-4 Problem 1 Solving a Problem with Parallel Lines
parallel | perpendicular | transversal | word problem | reasoning
DOK 2
D
PTS: 1
DIF: L3
3-4 Parallel and Perpendicular Lines
3-4.1 Relate parallel and perpendicular lines NAT:
G.3.b| G.3.g
3-4 Problem 1 Solving a Problem with Parallel Lines
parallel | perpendicular | transversal | word problem | reasoning
DOK 2
B
PTS: 1
DIF: L2
3-4 Parallel and Perpendicular Lines
3-4.1 Relate parallel and perpendicular lines STA:
MA.912.G.1.3
3-4 Problem 2 Proving a Relationship Between Two Lines
parallel lines | perpendicular lines | transversal
DOK: DOK 3
SHORT ANSWER
58. ANS:
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e. Addition Property of Equality
f. Division Property of Equality
PTS:
OBJ:
TOP:
KEY:
DOK:
59. ANS:
1
DIF: L3
REF: 2-5 Reasoning in Algebra and Geometry
2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
2-5 Problem 1 Justifying Steps When Solving an Equation
proof | deductive reasoning | Properties of Equality | multi-part question
DOK 2
Given
Addition Property of Equality
Simplify
Division Property of Equality
x = 27
Simplify
PTS: 1
DIF: L4
REF: 2-5 Reasoning in Algebra and Geometry
OBJ: 2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation
KEY: Properties of Equality | proof | deductive reasoning
DOK: DOK 3
60. ANS:
a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
PTS: 1
DIF: L3
REF: 2-5 Reasoning in Algebra and Geometry
OBJ: 2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation
KEY: deductive reasoning | proof | Properties of Equality
DOK: DOK 2
61. ANS:
a. 180
b. 180
c. Transitive Property (or Substitution Property)
d.
e.
PTS: 1
DIF: L3
REF: 2-6 Proving Angles Congruent
OBJ: 2-6.1 Prove and apply theorems about angles
STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
TOP: 2-6 Problem 2 Proof Using the Vertical Angles Theorem
KEY: Properties of Equality | deductive reasoning | proof | supplementary angles
DOK: DOK 2
62. ANS:
a. Corresponding angles
b. Vertical angles
c. Transitive Property
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.1 Prove theorems about parallel lines
STA: MA.912.G.1.3
TOP: 3-2 Problem 2 Proving an Angle Relationship
KEY: alternate interior angles | Alternate Interior Angles Theorem | proof | reasoning | two-column proof |
multi-part question DOK: DOK 2
63. ANS:
a. Vertical angles.
b. Transitive Property.
c. Alternate Interior Angles Converse.
PTS: 1
DIF: L3
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 2 Writing a Flow Proof of Theorem 3-6
KEY: two-column proof | proof | reasoning | corresponding angles | multi-part question
DOK: DOK 2
64. ANS:
The rowers keep corresponding angles congruent.
PTS: 1
DIF: L3
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 3 Determining Whether Lines are Parallel
KEY: transversal | word problem | reasoning | parallel lines
DOK: DOK 3
65. ANS:
Yes, Maple Street and Elm Street are parallel where River Drive crosses them.
and
are same-side
interior angles. If two lines and a transversal form same-side interior angles that are supplementary, then the
two lines are parallel (Converse of the Same-Side Interior Angles Theorem).
PTS: 1
DIF: L3
REF: 3-3 Proving Lines Parallel
OBJ: 3-3.1 Determine whether two lines are parallel
STA: MA.912.G.1.3| MA.912.G.8.5
TOP: 3-3 Problem 3 Determining Whether Lines are Parallel
KEY: Converse of Same-Side Interior Angles Theorem | parallel | word problem | transversal | reasoning
DOK: DOK 3
ESSAY
66. ANS:
[4] a. Given
b. Substitution Property
c. Vertical Angles Theorem
d. Substitution Property
[3] three parts correct
[2] two parts correct
[1] one part correct
PTS: 1
DIF: L4
REF: 2-6 Proving Angles Congruent
OBJ: 2-6.1 Prove and apply theorems about angles
STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
TOP: 2-6 Problem 2 Proof Using the Vertical Angles Theorem
KEY: Vertical Angles Theorem | proof | extended response | rubric-based question
DOK: DOK 3
67. ANS:
[4] By the definition of complementary angles,
and
By the Transitive Property of Equality (or Substitution Property),
. By the Subtraction Property of Equality,
by the definition of congruent angles.
OR
equivalent explanation
[3] one step missing OR one incorrect justification
[2] two steps missing OR two incorrect justifications
[1] correct steps with no explanations
PTS:
OBJ:
STA:
TOP:
KEY:
DOK:
68. ANS:
[4]
[3]
[2]
[1]
.
, and
1
DIF: L4
REF: 2-6 Proving Angles Congruent
2-6.1 Prove and apply theorems about angles
MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
2-6 Problem 3 Writing a Paragraph Proof
complementary angles | Properties of Equality | rubric-based question | extended response | proof
DOK 3
are supplementary, because it is given. So,
definition of supplementary angles.
because it is given. So,
definition of congruent angles. By the Substitution Property,
definition of supplementary angles,
are supplementary.
OR
equivalent explanation
one step missing OR one incorrect justification
two steps missing OR two incorrect justifications
correct steps with no explanations
PTS: 1
DIF: L4
REF: 2-6 Proving Angles Congruent
by the
by the
, so by the
OBJ: 2-6.1 Prove and apply theorems about angles
STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
TOP: 2-6 Problem 3 Writing a Paragraph Proof
KEY: complementary angles | supplementary angles | Properties of Equality | rubric-based question |
extended response | proof
DOK: DOK 3
69. ANS:
[4]
[3]
[2]
[1]
PTS:
OBJ:
TOP:
KEY:
angles
70. ANS:
[4]
[3]
[2]
[1]
PTS:
OBJ:
TOP:
KEY:
DOK:
OTHER
71. ANS:
[4]
correct idea, some details inaccurate
correct idea, some statements missing
correct idea, several steps omitted
1
DIF: L4
REF: 3-2 Properties of Parallel Lines
3-2.1 Prove theorems about parallel lines
STA: MA.912.G.1.3
3-2 Problem 2 Proving an Angle Relationship
two-column proof | proof | extended response | rubric-based question | parallel lines | supplementary
DOK:
DOK 3
By the definition of , r  s implies m2 = 90, and t  s implies m6 = 90. Line s
is a transversal. 2 and 6 are corresponding angles. By the Converse of the
Corresponding Angles Postulate, r || t.
correct idea, some details inaccurate
correct idea, not well organized
correct idea, one or more significant steps omitted
1
DIF: L4
REF: 3-4 Parallel and Perpendicular Lines
3-4.1 Relate parallel and perpendicular lines STA:
MA.912.G.1.3
3-4 Problem 2 Proving a Relationship Between Two Lines
paragraph proof | proof | reasoning | extended response | rubric-based question | perpendicular lines
DOK 3
OR
equivalent proof.
[3]
one step missing OR one incorrect justification
[2]
two steps missing OR two incorrect justifications
[1]
correct steps with no explanations
PTS: 1
DIF: L4
REF: 2-5 Reasoning in Algebra and Geometry
OBJ: 2-5.1 Connect reasoning in algebra and geometry
STA: MA.912.D.6.4| MA.912.G.8.5
TOP: 2-5 Problem 3 Writing a Two-Column Proof
KEY: Properties of Equality | proof
DOK: DOK 3
72. ANS:
Explanations may vary. Sample: If two angles are congruent and complementary, they have equal measures
that add to 90. Thus, each angle has a measure that is one-half of 90, or 45.
PTS: 1
DIF: L3
REF: 2-6 Proving Angles Congruent
OBJ: 2-6.1 Prove and apply theorems about angles
STA: MA.912.D.6.4| MA.912.G.8.1| MA.912.G.8.5
TOP: 2-6 Problem 3 Writing a Paragraph Proof
KEY: writing in math | complementary angles
DOK: DOK 2
73. ANS:
l and m are both perpendicular to n. Explanation: Because l and m are parallel,
are supplementary
by the Same-Side Interior Angles Theorem. It is given that
, so
180 = m1 + m2 = m1 + m1 = 2m1, and m1 = 90 = m2. Because 1 and 2 are right angles, l is
perpendicular to n and m is perpendicular to n.
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.1 Prove theorems about parallel lines
STA: MA.912.G.1.3
TOP: 3-2 Problem 2 Proving an Angle Relationship
KEY: perpendicular lines | reasoning | writing in math
DOK: DOK 3
74. ANS:
No. The angles for each corner form a 87º angle (37º + 50º). In order for the side pieces to be parallel, the sum
of the angle of the top piece and the angle of the side piece must be exactly 90º.
PTS: 1
DIF: L2
REF: 3-4 Parallel and Perpendicular Lines
OBJ: 3-4.1 Relate parallel and perpendicular lines STA:
MA.912.G.1.3
TOP: 3-4 Problem 1 Solving a Problem with Parallel Lines
KEY: parallel | perpendicular | word problem | reasoning
DOK: DOK 2
75. ANS:
Lines l and m are parallel. It is given that line k is parallel to line l and line k is parallel to line m Therefore,
line l is parallel to m, because in a plane, if two lines are parallel to the same line, then they are parallel to
each other.
PTS:
OBJ:
TOP:
KEY:
1
DIF: L3
REF: 3-4 Parallel and Perpendicular Lines
3-4.1 Relate parallel and perpendicular lines STA:
MA.912.G.1.3
3-4 Problem 2 Proving a Relationship Between Two Lines
parallel | perpendicular | word problem | reasoning
DOK: DOK 2