# 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 $\angle BAD = \angle BCD$.

## Proof

### Sufficient Condition

Let $ABCD$ be a parallelogram.

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

$\Box$

### Necessary Condition

Let $ABCD$ be such that:

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