Final answer:
The inverse of the alternate interior angles theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The inverse is true and can be proved by switching the hypothesis and conclusion of the original theorem.
Step-by-step explanation:
The inverse of the alternate interior angles theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The inverse of a theorem is formed by switching the hypothesis and conclusion of the original theorem. In this case, the original theorem states that if two lines are parallel, then the alternate interior angles are congruent.
Yes, the inverse of the alternate interior angles theorem is true. It can be proved by using the property that if two lines are parallel, then their alternate interior angles are congruent. By switching the hypothesis and conclusion, we can conclude that if the alternate interior angles are congruent, then the lines are parallel.
For example, if we have two lines cut by a transversal and we observe that the alternate interior angles are congruent, we can conclude that the lines are parallel according to the inverse of the alternate interior angles theorem.