5.04 Proving Lines Parallel

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Proving Lines Parallel Practice

Practice Problem #1

What must x equal for these lines to be parallel?

Line x is above line y and they are a pair of horizontal lines that are cut by a transversal. The angle to the upper left of the intersection with line y is 100 degrees. The angle to the bottom right of the intersection with line x has value x minus 15

What is the relationship between thse angles? Answer: alternate interior

Because they are on opposite sides of the transversal, they are alternate. Because they are contained between the two parallel lines, they are interior. So they are alternate interior angles.

Now that we know these are alternate interior angles, what is the relationship between these angles? Are they congruent, complementary, or supplementary? Answer: congruent

Alternate interior angles are congruent. Which equation should we use to solve for x?

x - 15 +100 = 90
x - 15 = 100
x - 15 + 100 = 180

Answer: x - 15 = 100

Now we just solve:

x - 15 = 100
x = 115

Practice Problem #2

What must x equal for these lines to be parallel?

Line x is above line y and they are a pair of horizontal lines that are cut by a transversal. The angle to the bottom left of the intersection with line x has value x + 5. The angle to the bottom left of the intersection with line y has value 75

What is the relationship between thse angles? Answer: same side interior

Because they are on the same side of the transversal, they are same side. Because they are contained between the two parallel lines, they are interior. So they are same side interior angles.

Now that we know these are same side interior angles, what is the relationship between these angles? Are they congruent, complementary, or supplementary? Answer: supplementary

Alternate interior angles are supplementary. Which equation should we use to solve for x?

x - 15 +75 = 90
x - 5 = 75
x + 5 + 75 = 180

Answer: x + 5 + 75 = 180

Since the angles are supplementary, and them together and set the sum equal to 180.

Now we just solve:

x - 5 + 75 = 180
x + 80 = 180
x = 100

Practice Problem #3

What must x equal for these lines to be parallel?

What is the relationship between thse angles? Answer: corresponding

Because they are on the same place in each set of angles, they are corresponding.

Now that we know these are corresponding angles, what is the relationship between these angles? Are they congruent, complementary, or supplementary? Answer: congruent

Alternate interior angles are congruent. Which equation should we use to solve for x?

2x + 80 = 90
2x = 80
2x + 80 = 180

Answer: 2x = 80

Since the angles are congruent, set them equal to one another to solve for x.

Now we just solve:

2x = 80
x = 40