Question

consider parallel lines cut by a transversal. explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Explanation:

First, the definition of vertical - angles states that vertical angles are congruent (e.g., ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8). The corresponding - angles postulate says that when parallel lines are cut by a transversal, corresponding angles are congruent (e.g., ∠1 and ∠5, ∠2 and ∠6). We can use the vertical - angles definition and the corresponding - angles postulate. For example, to show ∠2 and ∠7 are congruent: ∠2 and ∠4 are vertical angles so ∠2 = ∠4, and ∠4 and ∠7 are corresponding angles (since q || s and r is the transversal), so ∠4 = ∠7. By the transitive property of equality, ∠2 = ∠7.

Answer:

The vertical - angles definition and the corresponding - angles postulate can be used to prove that alternate exterior angles are congruent.