Exercise 15 Page 508

Let's draw a diagram, labeling a pair of alternate exterior angles — ∠ 1 and ∠ 2 — and another angle that we can relate to both of these, ∠ 3.

From the diagram we see that ∠ 1 and ∠ 3 are vertical angles. By the Vertical Angles Theorem, we know that these are congruent.

We can also see that ∠ 2 and ∠ 3 are corresponding angles. Since p ∥ q, we know by the Corresponding Angles Theorem that these angles are congruent.

Since ∠ 1≅ ∠ 3 and ∠ 3 ≅ ∠ 2, we can prove that ∠1 ≅ ∠ 2 using the Transitive Property of Congruence. Let's show this as a two-column proof.