Question

prove: ∠5≅∠6
j || k → given → ∠7≅∠6
transitive property
vertical angles
∠5≅∠6

Explanation:

Step1: Identify parallel - line property

Since $j\parallel k$, $\angle5\cong\angle7$ (corresponding angles postulate).

Step2: Identify vertical - angle property

$\angle7\cong\angle6$ because they are vertical angles.

Step3: Apply transitive property

If $\angle5\cong\angle7$ and $\angle7\cong\angle6$, then by the transitive property of congruence, $\angle5\cong\angle6$.

Answer:

$\angle5\cong\angle6$ is proved by using the corresponding - angles postulate for parallel lines $j$ and $k$ to get $\angle5\cong\angle7$ and the vertical - angles property to get $\angle7\cong\angle6$, and then the transitive property of congruence.