Sufficient Conditions for Quadrilaterals to Be Parallelograms

Theorem. Converse of the following: Opposite angles of a parallelogram are congruent.
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Prove this theorem as an exercise.

Theorem. Converse of the following: Consecutive angles in a parallelogram are supplementary.
If one angle of a quadrilateral is supplementary to both angles adjacent to it, then the quadrilateral is a parallelogram.