Answers2627 GEOMETRY ASlopes of Parallel and Perpendicular Lines

Slopes of Parallel and Perpendicular Lines — Unit test Answers

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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°.
25

Determine the missing information in the paragraph proof.Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).Prove: The slopes of perpendicular lines are negative reciprocals.

Question illustration
A
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1
Option A
B
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1
Option B
C
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1
Option C
D
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1
Option D
26

Consider the diagram.

Question illustration
A
intersecting.
B
parallel.
C
perpendicular.
D
skew.
27

In the diagram, DC is 10 units and BC is 6 units.

Question illustration
A
6 units
B
8 units
C
12 units
D
16 units
28

Two parallel lines are crossed by a transversal.

Question illustration
A
56.5°.
B
67.5°.
C
123.5°.
D
136.5°.
29

On a coordinate plane, 2 lines are shown. Line P Q has points (negative 5, 3) and (5, 1). Line R S has points (negative 4, negative 2) and (0, negative 4).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
30

In the diagram, CE=12 units and BE=5 units.

Question illustration
A
2 units
B
7 units
C
12 units
D
17 units
31

Consider the two planes.

Question illustration
A
line a.
B
line b.
C
line d.
D
plane Q.
33

Consider the diagram.

Question illustration
A
They lie in different planes and will never intersect.
B
They lie in the same plane but will never intersect.
C
They lie in different planes but will intersect if a plane is drawn to contain both lines.
D
They lie in different planes and will be parallel if a plane is drawn to contain both lines.
34

Question text not available

Question illustration
A
Option
Option A
B
Option
Option B
C
(8, –4)
D
(10, –7)
36

On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
37

A line contains points M(1, 3) and N(5, 0). What is the slope of MN?

A
negative StartFraction 4 Over 3 EndFraction
Option A
B
negative StartFraction 3 Over 4 EndFraction
Option B
C
StartFraction 3 Over 4 EndFraction
Option C
D
StartFraction 4 Over 3 EndFraction
Option D
38

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

Question illustration
A
2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 91 degrees. At the intersection with the second line, the bottom right angle is 91 degrees.
Option A
B
2 horizontal lines are intersected by another line. At the intersection with the first line, uppercase right angle is 91 degrees and the bottom left angle is 91 degrees.
Option B
C
2 horizontal lines are intersected by another line. At the intersection with the first line, the uppercase right angle is 89 degrees and the bottom right angle is 91 degrees.
Option C
D
2 horizontal lines are intersected by another line. At the intersection with the first line, the bottom right angle is 91 degrees. At the intersection with the second line, the top right angle is 89 degrees.
Option D
40

Segment CD is shown on the graph.

Question illustration
A
y = (3 – 1) + 1
Option A
B
y = (3 + 4) – 4
Option B
C
y = (3 – 1) + 1
Option C
D
y = (3 + 4) – 4
Option D

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