Free Geometry Worksheet
Proving that a Quadrilateral is a Parallelogram

The definition of a parallelogram gives one way to prove that a quadrilateral is a parallelogram (show both pair of opposite sides are parallel). Complete the following theorems which provide four more ways.

1) If both pairs of opposite sides of a quadrilateral are ___________________, then the quadrilateral is a parallelogram.

2) If one pairs of opposite sides of a quadrilateral are both ___________________ and ___________________, then the
quadrilateral is a parallelogram.

3) If both pairs of opposite angles of a quadrilateral are ___________________, then the quadrilateral is a parallelogram.

4) If the _________________ of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Decide whether each quadrilateral is a parallelogram. If the answer is yes, state the definition or theorem that applies.