Question

1. given - ∠5≅∠6 prove - ∠4≅∠7 statements reason 1. ∠5≅∠6 1. given 2. 2.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. $\angle4$ and $\angle5$ are vertical angles, so $\angle4\cong\angle5$. Also, $\angle6$ and $\angle7$ are vertical angles, so $\angle6\cong\angle7$.

Step2: Use the transitive property of congruence

Since $\angle5\cong\angle6$ (given) and $\angle4\cong\angle5$ and $\angle6\cong\angle7$ (vertical - angle property), by the transitive property of congruence, if $a = b$ and $b = c$, then $a = c$. So $\angle4\cong\angle7$.

Answer:

1. $\angle4\cong\angle5$, $\angle6\cong\angle7$; Reason: Vertical angles are congruent.