Question

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

Explanation:

Step1: Recall corresponding - angle property

Since \(p\parallel q\), corresponding angles are congruent. \(\angle1\) and \(\angle2\) are corresponding angles, so \(\angle1\cong\angle2\) (Corresponding - Angles Postulate).

Step2: Use given congruence

We are given that \(\angle1\cong\angle5\).

Step3: Apply transitive property of congruence

If \(\angle1\cong\angle2\) and \(\angle1\cong\angle5\), then by the transitive property of congruence (If \(a = b\) and \(a = c\), then \(b = c\)), we can conclude that \(\angle2\cong\angle5\).

Answer:

Statements	Reasons
2. \(\angle1\cong\angle2\)	Corresponding - Angles Postulate
3. \(\angle1\cong\angle5\)	Given
4. \(\angle2\cong\angle5\)	Transitive Property of Congruence