Question

select the correct answer from each drop - down menu. given: a || b prove: ∠1 ≅ ∠7 complete the proof. statements reasons 1. a || b given 2. ∠1 ≅ ∠5 corresponding angles theorem 3. ∠ ≅ ∠7 vertical angles theorem 4. ∠1 ≅ ∠ transitive property of congruence

Explanation:

Step1: Identify vertical - angle pair

By the vertical - angles theorem, $\angle5$ and $\angle7$ are vertical angles, so $\angle5\cong\angle7$.

Step2: Use transitive property

We know $\angle1\cong\angle5$ (corresponding angles) and $\angle5\cong\angle7$ (vertical angles). By the transitive property of congruence, $\angle1\cong\angle7$.

Answer:

1. $\angle5$; 4. $\angle7$