Parallelogram - Characterizations

Characterizations

A simple (non self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:

• Two pairs of opposite sides are equal in length.
• Two pairs of opposite angles are equal in measure.
• The diagonals bisect each other.
• One pair of opposite sides are parallel and equal in length.
• Adjacent angles are supplementary.
• Each diagonal divides the quadrilateral into two congruent triangles.
• The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law.)
• It has rotational symmetry of order 2.