Question

1. given: p||q; ∠1≅∠5 prove: ∠2≅∠5 statements reasons

Explanation:

Step1: State given information

$p\parallel q$, $\angle1\cong\angle5$ (Given)

Step2: Use corresponding - angles property

Since $p\parallel q$, $\angle1\cong\angle2$ (Corresponding angles postulate)

Step3: Apply transitive property of congruence

We know $\angle1\cong\angle5$ and $\angle1\cong\angle2$. By the transitive property of congruence, if $a = b$ and $a = c$, then $b = c$. So $\angle2\cong\angle5$.

Answer:

Statements	Reasons
2. $\angle1\cong\angle2$	Corresponding - angles postulate (because $p\parallel q$)
3. $\angle2\cong\angle5$	Transitive property of congruence