# parallelogram

A parallelogram^{} is a quadrilateral^{} whose opposite sides are parallel^{}.

Some special parallelograms have their own names: squares, rectangles^{}, rhombuses.
A rectangle is a parallelogram whose all angles are equal (i.e. ${90}^{\circ}$), a rhombus is a parallelogram whose all sides are equal, and a square is a parallelogram that is a rectangle and a rhombus at the same time.

Every parallelogram have their opposite sides and opposite angles equal. Also, adjacent^{} angles of a parallelogram always add up to ${180}^{\circ}$, and the diagonals^{} bisect each other.

A *base* of a parallelogram is one of its sides. Any side of a
parallelogram can be selected as its base. Once a base has been
selected, the *height* of the parallelogram is defined to be the
length of any line segment^{} perpendicular^{} to the base which extends
from the base to the opposite side parallel to the base. The area of
a parallelogram with base length $b$ and height $h$ is given by the
formula $A=bh$.

There is also a neat relation between the length of the sides and the lengths of the diagonals called the parallelogram law^{}.

Title | parallelogram |

Canonical name | Parallelogram |

Date of creation | 2013-03-22 12:02:21 |

Last modified on | 2013-03-22 12:02:21 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 11 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | ParallelogramTheorems |

Related topic | Quadrilateral |

Related topic | Rectangle |

Related topic | Rhombus |

Related topic | Square |

Related topic | ParallelogramLaw |

Related topic | Kite |

Related topic | Rhomboid^{} |

Related topic | ProofOfParallelogramTheorems |

Related topic | Parallelotope^{} |