Question

determining whether lines are parallel exercise 4 given: r || s and ∠1 is congruent to ∠3. prove: p || q

Explanation:

Step1: Use corresponding - angles property

Since \(r\parallel s\), \(\angle2\cong\angle3\) (corresponding angles).

Step2: Substitute using given congruence

Given \(\angle1\cong\angle3\), and \(\angle2\cong\angle3\), then \(\angle1\cong\angle2\) (transitive property of congruence).

Step3: Apply parallel - lines criterion

If \(\angle1\cong\angle2\), then \(p\parallel q\) (corresponding angles are congruent, so lines are parallel).

Answer:

Proved that \(p\parallel q\)