Question

proving parallel lines with alternate exterior angles
given: ∠1 ≅ ∠2
prove: p || q
angles lines statements reasons
≅ ∠1 ∠2 ∠3
statements reasons

1. ∠1 ≅ ∠2 1. given

Explanation:

Step1: Recall angle - line relationship

If alternate exterior angles are congruent, then the lines are parallel.

Step2: Identify angle type

\(\angle1\) and \(\angle2\) are alternate exterior angles.

Step3: Apply parallel - line theorem

Since \(\angle1\cong\angle2\) (given), by the alternate - exterior - angles converse theorem, \(p\parallel q\).

Answer:

1. \(p\parallel q\)

• Reason: Alternate - exterior - angles converse theorem (If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel)