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.

AI overview

A parallelogram is a four-sided shape where opposite sides are parallel to each other, which automatically makes those opposite sides equal in length and opposite angles equal in size. This shape is fundamental to Euclidean geometry because its defining properties depend directly on the parallel postulate, a cornerstone assumption of how geometry works in flat space.

AI-generated from the Wikipedia summary — may contain errors.

Key facts

Polygon.name: Parallelogram
Polygon.image: Parallelogram.svg
Polygon.caption: This parallelogram is a rhomboid as it has unequal sides and no right angles.
Polygon.type: Quadrilateral, Trapezium
Polygon.edges: 4
Polygon.symmetry: C2, [2]+,
Polygon.area: bh (base × height);ab sin θ (product of adjacent sides and sine of the vertex angle determined by them)
Polygon.properties: Convex polygon