Exercise 1 Page 514

Let's illustrate the example.

There are three angle pairs that have to be congruent if the lines are going to be parallel.

Corresponding Angles

According to the Corresponding Angles Converse, if two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel. We have four pairs of corresponding angles:

∠ 1 and ∠ 5, ∠ 2 and ∠ 6 ∠ 3 and ∠ 7, ∠ 4 and ∠ 8 .

Alternate Exterior Angles

According to the Alternate Exterior Angles Converse, if two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. Alternate exterior angles are outside of the lines and on opposite sides of the transversal. We have two pairs of such angles:

∠ 1 and ∠ 8, ∠ 2 and ∠ 7

Alternate Interior Angles

According to the Alternate Interior Angles Converse, if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. Alternate interior angles are between the lines and on opposite sides of the transversal. We have two pairs of such angles:

∠ 3 and ∠ 6, ∠ 4 and ∠ 5