AnswersLA-Geometry A Distance LearningProving Lines Parallel

Proving Lines Parallel — Unit test Answers

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21
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Letters w, x, y, and z are angle measures.

Question illustration
A
w
B
x
C
y
D
z
22
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Given: and Prove:

Question illustration
A
m∠1 = m∠4
B
m∠2 = m∠3
C
m∠1 + m∠4 = 180°
D
m∠2 + m∠3 = 180°
23

Determine the missing information in the paragraph proof.Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.Prove: Parallel lines have the same slope.

Question illustration
A
Option
Option A
B
Option
Option B
C
StartFraction v minus z + b Over x minus z + a EndFraction
Option C
D
StartFraction w minus x + a Over v minus z + b EndFraction
Option D
24

On a coordinate plane, line P Q goes through (negative 3, negative 3) and (3, negative 1). Point R is at (1, 1).

Question illustration
(
(0, )
Option (
(
(0, 4)
(
(, 0)
Option (
(
(4, 0)
25

Planes T and X are parallel. Plane T contains line a. Plane X contains line b.

Question illustration
A
They are skew and will never intersect.
B
They are parallel and will never intersect.
C
They are perpendicular and will intersect.
D
They will intersect at two points.
26

Given: and Prove: What is the missing reason in the proof?

Question illustration
A
given
B
transitive property
C
alternate interior angles theorem
D
converse alternate interior angles theorem
27

In the diagram, the length of segment QV is 15 units.

Question illustration
A
4 units
B
11 units
C
14 units
D
15 units
28

Two parallel lines are crossed by a transversal.

Question illustration
A
y = 40
B
y = 80
C
y = 100
D
y = 120
29

Two parallel lines are crossed by a transversal.

Question illustration
A
d = 55
B
d = 75
C
d = 125
D
d = 155
30

On a coordinate plane, line A B goes through (negative 2, 4) and (0, negative 4). Point Z is at (0, 2).

Question illustration
A
(–4, 1)
B
(1, –2 )
C
(2, 0)
D
(4, 4)
31

On a coordinate plane, line D F goes through points (negative 1, negative 3) and (2, 3). Point G is at (negative 4, negative 4).

Question illustration
A
(–2, 0)
B
(0, –2)
C
(0, 4)
D
(4, 0)
32

Horizontal lines e and f are cut by vertical lines a and b. At the intersection of lines a and e, the uppercase right angle is (x + 1) degrees. At the intersection of lines a and f, the bottom right angle is (x minus 3) degrees. At the intersection of lines b and e, the bottom left angle is y degrees.

Question illustration
A
87
B
88
C
91
D
92
33

Based on this information, which pair of lines, together, could be perpendicular to RS? Select two options.

A
Line E A
Option A
B
Line E R
Option B
C
Line E F
Option C
D
Line F G
Option D
E
Line F S
Option E
34

On a coordinate plane, 2 lines are shown. Line C D has points (negative 2, 4) and (0, negative 4). Line F G has points (negative 4, 0) and (4, 2).

Question illustration
A
They are perpendicular because their slopes are equal.
B
They are perpendicular because their slopes are negative reciprocals.
C
They are not perpendicular because their slopes are equal.
D
They are not perpendicular because their slopes are negative reciprocals.
35

On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2).

Question illustration
A
They are perpendicular because their slopes are equal.
B
They are perpendicular because their slopes are negative reciprocals.
C
They are not perpendicular because their slopes are equal.
D
They are not perpendicular because their slopes are not negative reciprocals.
36

Lines a and b are parallel lines cut by transversal f.

Question illustration
A
20°
B
70°
C
110°
D
130°
37

Consider the diagram.

Question illustration
A
corresponding angles theorem
B
alternate interior angles theorem
C
vertical angles theorem
D
alternate exterior angles theorem
38

Which diagram shows lines that must be parallel lines cut by a transversal?

A
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 65 degrees.
Option A
B
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the bottom left angle is 115 degrees and the bottom right angle is 65 degrees.
Option B
C
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the top right angle is 115 degrees. At the intersection of the second line with the third line, the uppercase left angle is 115 degrees.
Option C
D
2 horizontal lines are intersected by a third line. At the intersection of the first line with the third line, the uppercase left angle is 65 degrees and the bottom right angle is 65 degrees.
Option D
39

A pipe cleaner lay across a wire shelf. The wires that make up the shelf are parallel, and the pipe cleaner is a transversal. The parallel wires are labeled a, b, and, c, and the angles are labeled with numbers.

Question illustration
A
They are same-side interior angles, so angle 3 measures 50°.
B
They are alternate interior angles, so angle 3 also measures 130°.
C
They are corresponding angles, so angle 3 also measures 130°.
D
They are alternate exterior angles, so angle 3 measures 50°.
40

Consider the diagram.

Question illustration
A
intersecting.
B
parallel.
C
perpendicular.
D
skew.

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