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.

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