Parallelogram
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.
| Parallelogram | |
|---|---|
This parallelogram is a rhomboid as it has no right angles and unequal sides. | |
| Type | quadrilateral, trapezium |
| Edges and vertices | 4 |
| Symmetry group | C2, [2]+, |
| Area | b × h (base × height); ab sin θ (product of adjacent sides and sine of the vertex angle determined by them) |
| Properties | convex |
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 etymology (in Greek παραλληλ-όγραμμον, parallēl-ógrammon, a shape "of parallel lines") reflects the definition.