Question

alternate interior angles of parallel lines theorem
if two lines are parallel, then the alternate interior
angles are congruent.
write the converse of this theorem.

Explanation:

Step1: Identify the hypothesis and conclusion of the original theorem

The original theorem is "If two lines are parallel, THEN the alternate interior angles are congruent." Here, the hypothesis is "two lines are parallel" and the conclusion is "alternate interior angles are congruent".

Step2: Swap the hypothesis and conclusion for the converse

To find the converse, we swap the hypothesis and the conclusion.

Answer:

If alternate interior angles are congruent, then two lines are parallel.