Alternate Interior Angles Theorem Converse

We have shown that when two parallel lines are intersected by a transversal line the interior alternating angles and exterior alternating angles are congruent that is they have the same measure of the angle.

Alternate interior angles theorem converse. The alternate interior angles theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congruent. In today s geometry lesson we ll prove the converse of the alternate interior angles theorem. Converse of the alternate interior angles theorem.

Alternate interior angles examples we can prove both these theorems so you can add them to your toolbox. A theorem is a proven statement or an. This does happen to be true and can be a useful way to prove that lines are parallel.

Let s recall the alternate interior angles theorem. If alternate interior angles formed by two lines with an intersecting traversal are congruent then these two lines are parallel. So in the figure below if k l then 2 8 and 3 5.

In this video i take students through an example that using the converse of the corresponding angles postulate to prove the converse of the alternate interior angle theorem. Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel.