Properties and characteristics of parallelograms

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. This leads to several important geometric properties that can be used in problem solving.

Important properties

• Opposite sides are equal in length: $AB = CD$ and $BC = DA$.

• Opposite angles are equal: $\angle ABC = \angle CDA$, $\angle BAD = \angle BCD$.

• Consecutive angles are supplementary: $\angle BAD + \angle ABC = 180^\circ$.

• Diagonals bisect each other: The point where the diagonals cross divides each diagonal into two equal parts.

• Each diagonal splits the parallelogram into two congruent triangles.