Answers 25-26 MATH 1 - S1Slopes of Parallel and Perpendicular Lines

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

Line E A

Line E R

Line E F

Line F G

Line F S

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Consider the diagram.

intersecting.

parallel.

perpendicular.

skew.

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

6 units

8 units

12 units

16 units

Two parallel lines are crossed by a transversal.

56.5°.

67.5°.

123.5°.

136.5°.

Consider the diagram.

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

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).

They are parallel because their slopes are equal.

They are parallel because their slopes are negative reciprocals.

They are not parallel because their slopes are not equal.

They are not parallel because their slopes are negative reciprocals.

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).

They are perpendicular because their slopes are equal.

They are perpendicular because their slopes are negative reciprocals.

They are not perpendicular because their slopes are equal.

They are not perpendicular because their slopes are not negative reciprocals.

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

2 units

7 units

12 units

17 units

Consider the two planes.

line a.

line b.

line d.

plane Q.

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.

The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height.

−3

Option

Consider the diagram.

They lie in different planes and will never intersect.

They lie in the same plane but will never intersect.

They lie in different planes but will intersect if a plane is drawn to contain both lines.

They lie in different planes and will be parallel if a plane is drawn to contain both lines.

The table represents a linear function.

–

–8

–

–4

Question text not available

Option

(8, –4)

(10, –7)

Two parallel lines are crossed by a transversal.

y = 40

y = 80

y = 100

y = 120

In the diagram, the length of segment TR can be represented by 5x – 4.

3 units

11 units

13 units

15 units

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

4 units

11 units

14 units

15 units

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).

They are parallel because their slopes are equal.

They are parallel because their slopes are negative reciprocals.

They are not parallel because their slopes are not equal.

They are not parallel because their slopes are negative reciprocals.

Which of these values could be the slope of the line? Select two options.

–2

Option

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

negative StartFraction 4 Over 3 EndFraction

negative StartFraction 3 Over 4 EndFraction

StartFraction 3 Over 4 EndFraction

StartFraction 4 Over 3 EndFraction

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

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.

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.

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.

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.

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

20°

70°

110°

130°

The table represents a linear function.

–

–10

–

–5

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R is at (4, 2).

(–6, 10)

(–4, –8)

(0, –1)

(2, 4)

Segment CD is shown on the graph.

y = (3 – 1) + 1

y = (3 + 4) – 4

y = (3 – 1) + 1

y = (3 + 4) – 4

The given line segment has a midpoint at (3, 1).

y = x

y = x – 2

y = 3x

y = 3x − 8

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.

Tracie’s bus travels towards her home at an average speed of mile per minute.

Tracie’s bus travels towards her home at an average speed of 2 miles per minute.

Tracie’s bus travels away from her home at an average speed of mile per minute.

Tracie’s bus travels away from her home at an average speed of 2 miles per minute.

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).

They are perpendicular because their slopes are equal.

They are perpendicular because their slopes are negative reciprocals.

They are not perpendicular because their slopes are equal.

They are not perpendicular because their slopes are negative reciprocals.

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

Option

The table represents a linear function.

–3

–2

Given: and g is a transversalProve:

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

Consider the incomplete paragraph proof.Given: P is a point on the perpendicular bisector, l, of MN.Prove: PM = PN

point M

point Q

segment PM

segment QM

On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3).

x + 2y = 4

x + 2y = 8

2x + y = 4

2x + y = 8

Two parallel lines are crossed by a transversal.

h = 60

h = 80

h = 100

h = 120

Which statements are true about triangle XYZ? Select three options.

XY measures units.

YZ measures units.

ZX measures units.

XYZ is a right triangle.

XYZ is a scalene triangle.

Lines e and f are intersected by line a. At the intersection of lines a and e, the bottom right angle is 72 degrees. At the intersection of lines a and f, the uppercase right angle is 108 degrees.

alternate interior angles theorem

same side interior angles theorem

converse of the alternate interior angles theorem

converse of the same side interior angles theorem

In the diagram, g ∥ h, m∠1 = (4x + 36)°, andm∠2 = (3x – 3)°.

21°

60°

120°

159°

Silvio wants to find the perimeter of quadrilateral ABCD. He begins by computing the length of side AB using the distance formula. Finish Silvio’s work to find the length of side AB.What is the perimeter of quadrilateral ABCD?

15 units

17 units

18 units

20 units

A given line has the equation .What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?

Option

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

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

given

transitive property

alternate interior angles theorem

converse alternate interior angles theorem

Janelle says that lines l and m are skew lines.

Yes, because the lines are not parallel.

Yes, because the lines will intersect.

No, because the lines are in the same plane.

No, because the lines are perpendicular.

Two parallel lines are crossed by a transversal.

d = 55

d = 75

d = 125

d = 155

Two parallel lines are crossed by a transversal.

x = 45

x = 65

x = 95

x = 115 ✓ Correct

The given line passes through the points (0, ) and (2, 3).

Option

In the diagram, the length of segment TQ is 40 units.

32 units

36 units

40 units

44 units

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

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.

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.

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.

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.

Lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase right angle is 110 degrees. At the intersection of lines b and e, the uppercase right angle is 110 degrees. At the intersection of lines b and f, the bottom right angle is 80 degrees.

Lines a and b are parallel because their corresponding angles are congruent.

Lines a and b are parallel because their same side exterior angles are congruent.

Lines e and f are parallel because their corresponding angles are congruent.

Lines e and f are parallel because their same side exterior angles are supplementary.

On a coordinate plane, a line goes through (negative 5, negative 4) and (0, negative 3). A point is at (negative 2, 2).

y = x + 4

y = x +

y = –5x + 4

y = –5x +

Kevin says that lines p and m will eventually intersect.

No, because they are non-coplanar.

No, because they are parallel.

Yes, because they are perpendicular.

Yes, because they are coplanar.

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.

They are same-side interior angles, so angle 3 measures 50°.

They are alternate interior angles, so angle 3 also measures 130°.

They are corresponding angles, so angle 3 also measures 130°.

They are alternate exterior angles, so angle 3 measures 50°.

Lines a and b are parallel and lines e and f are parallel.

179

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

(–4, 1)

(1, –2 )

(2, 0)

(4, 4)

In the diagram shown, the distance between points A and C is the same as the distance between points B and G.

non-coplanar.

parallel.

perpendicular.

skew.

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).

(–2, 0)

(0, –2)

(0, 4)

(4, 0)

Two parallel lines are crossed by a transversal.

y = 30

y = 50

y = 110

y = 130

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.

(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1

(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1

(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1

(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1

Two parallel lines are crossed by a transversal.

a = 43

a = 63 ✓ Correct

a = 117

a = 137

The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio?

–16

–11

–4

–1

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