In the parallelogram the diagonal is drawn.
According to the definition of a parallelogram, the opposite sides are parallel, and
Then, by the Alternate Interior Angles Theorem, the angles and
Since the triangles have two congruent angles and share one side, the ASA Congruence Theorem applies. It states that two triangles are congruent if two angles and their including side are congruent. As the triangles are congruent, all their corresponding parts are congruent. Therefore, the angles and are congruent as well.
Since the angles and are the sum of the same two congruent angles, they are congruent.
The proof can be summarized in a flowchart proof.