Question

e alternate exterior angles converse, which states that if two parallel lines are cut by a transversal, then the alternate exterior angles are
∠1≅∠7 and ∠2≅∠8

use the alternate exterior angles converse, use a two - column proof.
statements reasons
∠3≅∠5 and ∠4≅∠6 1. given
∠1≅∠5,∠2≅∠6,∠3≅∠7, and ∠4≅∠8 2. alternate interior angles converse
3.

Explanation:

Step1: Recall angle - congruence properties

Vertical angles are congruent. $\angle1$ and $\angle3$ are vertical angles, so $\angle1\cong\angle3$; $\angle2$ and $\angle4$ are vertical angles, so $\angle2\cong\angle4$; $\angle5$ and $\angle7$ are vertical angles, so $\angle5\cong\angle7$; $\angle6$ and $\angle8$ are vertical angles, so $\angle6\cong\angle8$.

Step2: Use transitive property

Since $\angle3\cong\angle5$ and $\angle1\cong\angle3$, by the transitive property of congruence, $\angle1\cong\angle5$. Similarly, since $\angle4\cong\angle6$ and $\angle2\cong\angle4$, $\angle2\cong\angle6$. Also, since $\angle3\cong\angle7$ and $\angle3\cong\angle5$, $\angle5\cong\angle7$ and since $\angle4\cong\angle8$ and $\angle4\cong\angle6$, $\angle6\cong\angle8$.

Step3: Justify the third - row reason

The reason for the third row is "Transitive Property of Congruence".

Answer:

Transitive Property of Congruence