# Parallelogram

## Quadrilateral with two pairs of parallel sides / From Wikipedia, the free encyclopedia

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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.

**Quick Facts**Type, Edges and vertices ...

Parallelogram | |
---|---|

Type | quadrilateral, trapezium |

Edges and vertices | 4 |

Symmetry group | C_{2}, [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 word comes from the Greek παραλληλό-γραμμον, *parallēló-grammon*, which means a shape "of parallel lines".