Question

which diagram represents the hypothesis of the converse of corresponding angles theorem? (three diagrams showing lines and transversals with angles marked)

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.

Step2: Analyze each diagram

• In the first diagram, there are two lines \(m\) and \(n\) cut by a transversal. The corresponding angles are marked as congruent.
• In the second diagram, the angles marked are not corresponding angles.
• In the third diagram, the angles marked are not corresponding angles.

Answer:

The first diagram.