Quadrilateral is Parallelogram iff Both Pairs of Opposite Angles are Equal

Theorem
Let $ABCD$ be a quadrilateral.

Then:
 * $ABCD$ is a parallelogram


 * $\angle ABC = \angle ADC$ and $\angle BAD = \angle BCD$.
 * $\angle ABC = \angle ADC$ and $\angle BAD = \angle BCD$.

Sufficient Condition
Let $ABCD$ be a parallelogram.

Then by Opposite Sides and Angles of Parallelogram are Equal:
 * $\angle ABC = \angle ADC$ and $\angle BAD = \angle BCD$.

Necessary Condition
Let $ABCD$ be such that:


 * $\angle ABC = \angle ADC$ and $\angle BAD = \angle BCD$.