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In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.

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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 is parallel and equal in length.

Adjacent angles are supplementary.

Each diagonal divides the quadrilateral into two congruent triangles.

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