Parallelogram

Parallelogram
This parallelogram is a rhomboid as it has unequal sides and no right angles.
Type	Quadrilateral, Trapezium
Edges and vertices	4
Symmetry group	C2, [2]+,
Area	bh (base × height); ab sin θ (product of adjacent sides and sine of the vertex angle determined by them)
Properties	Convex polygon

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.

By comparison, a quadrilateral with at least one pair of parallel sides is a trapezoid in American English or a trapezium in British English.

The three-dimensional counterpart of a parallelogram is a parallelepiped.

The word "parallelogram" comes from the Greek παραλληλό-γραμμον, parallēló-grammon, which means "a shape of parallel lines".