Question

prove the alternate exterior angles converse, which states that if two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. given: n||m prove: ∠1≅∠7 and ∠2≅∠8 to prove the alternate exterior angles converse, use a two - column proof. statements reasons 1. n||m 1. given 2. ∠3≅∠5 and ∠4≅∠6 2. alternate interior angles converse 3. ∠1≅∠5, ∠2≅∠6, ∠3≅∠7, and ∠4≅∠8 3.

Explanation:

Step1: Identify angle - pair relationships

We know that vertical angles are congruent. In the given figure, $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$ are vertical - angle pairs.

Step2: Justify the congruence

Since vertical angles are always congruent by the Vertical Angles Theorem, we can state that $\angle1\cong\angle5$, $\angle2\cong\angle6$, $\angle3\cong\angle7$, and $\angle4\cong\angle8$.

Answer:

1. Vertical Angles Theorem