Question

name
date:
period:
parallel and perpendicular lines test
directions: circle the best answer for each question.

1. which type of special angle pair is shown?

a. corresponding
b. alternate exterior
c. consecutive interior
d. alternate interior

1. write the equation of a line that is parallel to

y = 2x - 10 and passes through the point (2, -7).
a. y = -\frac{1}{2}x - 6
b. y = 2x - 6
c. y = -\frac{1}{2}x - 11
d. y = 2x - 11

1. solve for x.

a. x = 46.7
b. x = 20
c. x = 40
d. x = 53.3

1. fill in the blanks.

the slopes of parallel lines are ________. the slopes of perpendicular lines are ________.
a. opposite reciprocals, equal
b. opposite reciprocals, consecutive
c. equal, opposite reciprocals
d. equal, adjacent

1. are the lines parallel, perpendicular, or neither?

line a: 4x + 6y = 12
line b: 2x + 3y = 9
a. parallel
b. perpendicular
c. neither

1. find the measure of the missing angle.

a. 132°
b. 68°
c. 87°
d. 48°

1. what is the correct missing reason that will complete this proof?

a. substitution
b. corresponding angles
c. cpctc
d. definition of congruent
given: lines g and h are parallel lines cut by a transversal
prove: ∠1 ≅ ∠5 (corresponding angles are congruent)

1. lines g and h are parallel lines cut by a transversal 1. given
2. ∠1 ≅ ∠4 2. vertical angles
3. ∠4 ≅ ∠5 3. alternate interior angles
4. ∠1 ≅ ∠5 4.

Explanation:

Step1: Find the slope of the given line

The equation of the given line is \(y = 2x-10\), which is in the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept). So, the slope \(m = 2\).
Since parallel lines have equal slopes, the slope of the line we want to find is also \(m = 2\).

Step2: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(2,-7)\) and \(m = 2\).
Substitute the values into the formula:

$$
LATEXBLOCK0
$$

Answer:

d. \(y = 2x-11\)