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Triangle Angle Theorems Answers

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Two parallel lines are crossed by a transversal.

y = 40

y = 80

y = 100

y = 120

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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

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

4 units

11 units

14 units

15 units

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

y = x

y = x – 2

y = 3x

y = 3x − 8

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 a and b are parallel lines cut by transversal f.

20°

70°

110°

130°

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)

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

Option

Two parallel lines are crossed by a transversal.

d = 55

d = 75

d = 125

d = 155

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.

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.

Consider the diagram.

intersecting.

parallel.

perpendicular.

skew.

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

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 +

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°.

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)

Consider the diagram.

corresponding angles theorem

alternate interior angles theorem

vertical angles theorem

alternate exterior angles theorem

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

2 units

7 units

12 units

17 units

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.