Question

1. fill in the missing steps of the proof of the converse of the alternate exterior angles theorem. given: ∠1≅∠7 prove: a∥b 1) ∠1≅∠7 1) given 2) ∠1≅∠5 2) vertical angles theorem 3) a∥b

Explanation:

Step1: Given information

We are given that $\angle1\cong\angle7$.

Step2: Use vertical - angle property

$\angle7\cong\angle5$ because vertical angles are congruent.

Step3: Transitive property of congruence

Since $\angle1\cong\angle7$ and $\angle7\cong\angle5$, then $\angle1\cong\angle5$ by the transitive property of congruence.

Step4: Converse of alternate - exterior angles theorem

If $\angle1\cong\angle5$ (alternate - exterior angles), then $a\parallel b$ by the converse of the alternate - exterior angles theorem.

Answer:

1. Given: $\angle1\cong\angle7$
2. Vertical Angles Theorem: $\angle7\cong\angle5$
3. Transitive Property of Congruence: $\angle1\cong\angle5$
4. Converse of Alternate Exterior Angles Theorem: $a\parallel b$