2. Example 2: Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
1 and 5
B. alternate interior angles
3 and 5
C. alternate exterior angles
1 and 7
D. same-side interior angles
3 and 6

3. Warm Up
Identify each angle pair.
1. 1 and 3
2. 3 and 6
3. 4 and 5
4. 6 and 7
corr. s
alt. int. s
alt. ext. s
same-side int s

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

6. Example 1: Using the Corresponding Angles Postulate
Find each angle measure.
A. mECF
x = 70
Corr. s Post.
mECF = 70°
B. mDCE
5x = 4x + 22
Corr. s Post.
x = 22
Subtract 4x from both sides.
mDCE = 5x
= 5(22)
Substitute 22 for x.
= 110°

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

9. 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.

11. Example 4: Carpentry Application
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.