Parallelogram

In <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a>, a parallelogram is a <a href="/facts/Simple_polygon/C5CfrPWf">simple</a> (non-<a href="/facts/List_of_self-intersecting_polygons/zySCnDLM">self-intersecting</a>) <a href="/facts/Quadrilateral/QCGqrkp2">quadrilateral</a> with two pairs of <a href="/facts/Parallel_(geometry)/16r5yq7D">parallel</a> 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 <a href="/facts/Congruence_(geometry)/2tKJ6AhB">congruence</a> of opposite sides and opposite angles is a direct consequence of the Euclidean <a href="/facts/Parallel_postulate/xhSxUX4u">parallel postulate</a> 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 <a href="/facts/Trapezoid/nCBKsauz">trapezoid</a> in American English or a trapezium in British English.
The three-dimensional counterpart of a parallelogram is a <a href="/facts/Parallelepiped/Qn7cDgSr">parallelepiped</a>.
The word "parallelogram" comes from the Greek παραλληλό-γραμμον, parallēló-grammon, which means "a shape of parallel lines".

Parallelogram open-in-new

Parallelogram