If a quadrilateral has both pairs of opposite sides congruent then it is a parallelogram.

Theorem 5.2:

If a quadrilateral has one pair of opposite sides that are both congruent and parallel then it is a parallelogram.

Theorem 5.3:

If a quadrilateral has both pairs of opposite angles congruent then it is a parallelogram.

Theorem 5.4:

If a quadrilateral has one pair of opposite angles congruent and one pair of opposite sides parallel then it is a parallelogram.

Theorem 5.5:

If a quadrilateral’s diagonals bisect each other then it is a parallelogram.

Theorem 5.6:

The converse of Theorem 5.1.

Theorem 5.7:

The converse of Theorem 5.3.

Theorem 5.8:

The converse of Theorem 5.5.