Example 2: Classifying Pairs of Angles

Give an example of each angle pair.

A. corresponding angles

B. alternate interior angles

C. alternate exterior angles

1 and 5

D. same-side interior angles

3 and 5

1 and 7

3 and 6

Warm UpIdentify each angle pair.

1. 1 and 3

2. 3 and 6

3. 4 and 5

4. 6 and 7 same-side int s

corr. s

alt. int. s

alt. ext. s

Prove and use theorems about the angles formed by parallel lines and a transversal.

Objective

Find each angle measure.

Example 1: Using the Corresponding Angles Postulate

A. mECF

x = 70

B. mDCE

mECF = 70°

Corr. s Post.

5x = 4x + 22 Corr. s Post.

x = 22 Subtract 4x from both sides.

mDCE = 5x

= 5(22) Substitute 22 for x.

= 110°

If a transversal is perpendicular to two parallel lines, all eight angles are congruent.

Helpful Hint

The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.

Example 4: Carpentry ApplicationA carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.