Question

which diagram represents the hypothesis of the converse of corresponding angles theorem?

Explanation:

Step1: Recall the converse of corresponding angles theorem

The converse of the corresponding angles theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. The hypothesis is about the congruence of corresponding angles.

Step2: Analyze each diagram

• In the first diagram (with lines \(m\) and \(n\)), the marked angles are corresponding angles and they are congruent.
• In the second diagram (with lines \(p\) and \(q\)), the marked angles are vertical angles.
• In the third diagram (with lines \(x\) and \(y\)), the marked angles are alternate interior angles.

Answer:

The first diagram.