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.
Read more about this topic: Parallelogram