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 1. n||m 2. ∠3≅∠5 and ∠4≅∠6 reasons 1. given 2. alternate interior angles converse vertical angles theorem linear pair theorem corresponding angles converse

Explanation:

Step1: Recall parallel - line properties

Since \(n\parallel m\), when two parallel lines are cut by a transversal, alternate interior angles are congruent. \(\angle3\) and \(\angle5\), \(\angle4\) and \(\angle6\) are alternate interior angles.

Step2: Identify the reason

The reason for \(\angle3\cong\angle5\) and \(\angle4\cong\angle6\) is the Alternate Interior Angles Converse.

Answer:

Alternate Interior Angles Converse