This article is about the quadrilateral shape. For the album by Linda Perhacs, see Parallelograms (album).
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
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 comes from the Greek παραλληλό-γραμμον, parallēló-grammon, which means a shape "of parallel lines".
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