# Difference between revisions of "Quadrilateral"

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− | A quadrilateral is a [[polygon]] with four sides. | + | A '''quadrilateral''' is a [[polygon]] with four sides. |

− | As a consequence of the definition, the sum of the angles in a quadrilateral equals 360<sup> | + | As a consequence of the definition, the sum of the angles in a quadrilateral equals 360<sup>o</sup>, and all quadrilaterals are capable of [[tessellation|tessellating]] an [[infinite]] plane. |

− | + | ==Classification of Quadrilaterals== | |

The [[classification]] of quadrilaterals is complex, as there are several intersecting sub-categories: | The [[classification]] of quadrilaterals is complex, as there are several intersecting sub-categories: | ||

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* A [[rhombus]] has four equal sides | * A [[rhombus]] has four equal sides | ||

* A [[kite]] has two pairs of adjacent equal sides | * A [[kite]] has two pairs of adjacent equal sides | ||

− | * A [[re-entrant quadrilateral]] has one internal angle greater than 180<sup> | + | * A [[re-entrant quadrilateral]] has one internal angle greater than 180<sup>o</sup>; this may be contrasted with a [[convex quadrilateral]] in which all internal angles are less than 180<sup>o</sup> |

* An [[arrowhead]] is a re-entrant [[kite]] | * An [[arrowhead]] is a re-entrant [[kite]] | ||

* A [[square]] is both a [[rectangle]] and a [[rhombus]] | * A [[square]] is both a [[rectangle]] and a [[rhombus]] | ||

− | + | [[Category:Plane Geometry]] | |

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− | [[Category:Geometry]] | + |

## Latest revision as of 12:03, 13 July 2016

A **quadrilateral** is a polygon with four sides.

As a consequence of the definition, the sum of the angles in a quadrilateral equals 360^{o}, and all quadrilaterals are capable of tessellating an infinite plane.

## Classification of Quadrilaterals

The classification of quadrilaterals is complex, as there are several intersecting sub-categories:

- A (British) trapezium or (American) trapezoid has one pair of opposite sides parallel. A version of this called the isosceles trapezium has the other pair of opposite sides equal
- A parallelogram has two pairs of opposite sides parallel (and equal)
- A rectangle has four right angles
- A rhombus has four equal sides
- A kite has two pairs of adjacent equal sides
- A re-entrant quadrilateral has one internal angle greater than 180
^{o}; this may be contrasted with a convex quadrilateral in which all internal angles are less than 180^{o} - An arrowhead is a re-entrant kite
- A square is both a rectangle and a rhombus