## Quadrilateral |

Quadrilateral | |
---|---|

Some types of quadrilaterals | |

4 | |

{4} (for square) | |

various methods; see below | |

90° (for square and rectangle) |

In **quadrilateral** is a **quadrangle** is used, by analogy with **tetragon** for consistency with

The origin of the word "quadrilateral" is the two Latin words *quadri*, a variant of four, and *latus*, meaning "side".

Quadrilaterals are

The *ABCD* add up to 360

This is a special case of the *n*-gon interior angle sum formula (*n* − 2) × 180°.

All non-self-crossing quadrilaterals

- simple quadrilaterals
- complex quadrilaterals
- special line segments
- area of a convex quadrilateral
- diagonals
- angle bisectors
- bimedians
- trigonometric identities
- inequalities
- maximum and minimum properties
- remarkable points and lines in a convex quadrilateral
- other properties of convex quadrilaterals
- taxonomy
- skew quadrilaterals
- see also
- references
- external links

Any quadrilateral that is not self-intersecting is a simple quadrilateral.

In a convex quadrilateral, all interior angles are less than 180° and the two diagonals both lie inside the quadrilateral.

- Irregular quadrilateral (
British English ) or trapezium (North American English ): no sides are parallel. (In British English thiswas once called a .)*trapezoid* Trapezium (UK) ortrapezoid (US): at least one pair of opposite sides areparallel . Trapezia (UK) and trapezoids (US) include parallelograms.Isosceles trapezium (UK) orisosceles trapezoid (US): one pair of opposite sides are parallel and the baseangles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length.Parallelogram : a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms include rhombi (including those rectangles we call squares) and rhomboids (including those rectangles we call oblongs). In other words, parallelograms include all rhombi and all rhomboids, and thus also include all rectangles.Rhombus or rhomb: all four sides are of equal length. An equivalent condition is that the diagonals perpendicularly bisect each other. Informally: "a pushed-over square" (but strictly including a square, too).Rhomboid : a parallelogram in which adjacent sides are of unequal lengths and some angles areoblique (equivalently, having no right angles). Informally: "a pushed-over oblong". Not all references agree, some define a rhomboid as a parallelogram which is not a rhombus.^{[1]}Rectangle : all four angles are right angles. An equivalent condition is that the diagonals bisect each other and are equal in length. Rectangles include squares and oblongs. Informally: "a box or oblong" (including a square).Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), that the diagonals perpendicularly bisect each other, and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle (four equal sides and four equal angles).Oblong : a term sometimes used to denote a rectangle which has unequal adjacent sides (*i.e.*a rectangle that is not a square).^{[2]}Kite : two pairs of adjacent sides are of equal length. This implies that one diagonal divides the kite intocongruent triangles , and so the angles between the two pairs of equal sides are equal in measure. It also implies that the diagonals are perpendicular. Kites include rhombi.

Tangential quadrilateral : the four sides are tangents to an inscribed circle. A convex quadrilateral is tangential if and only if opposite sides have equal sums.Tangential trapezoid : a trapezoid where the four sides aretangents to aninscribed circle .Cyclic quadrilateral : the four vertices lie on acircumscribed circle . A convex quadrilateral is cyclic if and only if opposite angles sum to 180°.Right kite : a kite with two opposite right angles. It is a type of cyclic quadrilateral.Bicentric quadrilateral : it is both tangential and cyclic.Orthodiagonal quadrilateral : the diagonals cross atright angles .Equidiagonal quadrilateral : the diagonals are of equal length.Ex-tangential quadrilateral : the four extensions of the sides are tangent to anexcircle .- An
*equilic quadrilateral*has two opposite equal sides that, when extended, meet at 60°. - A
*Watt quadrilateral*is a quadrilateral with a pair of opposite sides of equal length.^{[3]} - A
*quadric quadrilateral*is a convex quadrilateral whose four vertices all lie on the perimeter of a square.^{[4]} - A
*diametric quadrilateral*is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle.^{[5]} - A
*Hjelmslev quadrilateral*is a quadrilateral with two right angles at opposite vertices.^{[6]}

In a concave quadrilateral, one interior angle is bigger than 180° and one of the two diagonals lies outside the quadrilateral.

- A
*dart*(or arrowhead) is aconcave quadrilateral with bilateral symmetry like a kite, but one interior angle is reflex. See(concave) kite .

Other Languages

Afrikaans: Vierhoek

አማርኛ: አራት ማዕዘን

العربية: رباعي الأضلاع

অসমীয়া: চতুৰ্ভুজ

asturianu: Cuadriláteru

azərbaycanca: Dördbucaqlı

বাংলা: চতুর্ভুজ

Bân-lâm-gú: Sì-kak-hêng

беларуская: Чатырохвугольнік

беларуская (тарашкевіца): Чатырохкутнік

български: Четириъгълник

bosanski: Četverougao

brezhoneg: Pevarc'hostezeg

català: Quadrilàter

Чӑвашла: Тăват кĕтеслĕх

čeština: Čtyřúhelník

chiShona: Gonyoina

dansk: Firkant

davvisámegiella: Njealječiegat

Deutsch: Viereck

eesti: Nelinurk

Ελληνικά: Τετράπλευρο

español: Cuadrilátero

Esperanto: Kvarlatero

euskara: Lauki

فارسی: چهارضلعی

français: Quadrilatère

Gàidhlig: Ceithir-cheàrnach

galego: Cuadrilátero

한국어: 사각형

Հայերեն: Քառանկյուն

हिन्दी: चतुर्भुज

hrvatski: Četverokut

Ido: Quadrilatero

íslenska: Ferhyrningur

italiano: Quadrilatero

עברית: מרובע

Basa Jawa: Quadrilateral

ქართული: ოთხკუთხედი

қазақша: Төртбұрыш

Kiswahili: Pembenne

kurdî: Çargoşe

latviešu: Četrstūris

lietuvių: Keturkampis

Limburgs: Veerhook

lumbaart: Quadrilàter (geometrìa)

magyar: Négyszög

македонски: Четириаголник

മലയാളം: ചതുർഭുജം

मराठी: चौकोन

Bahasa Melayu: Segi empat

မြန်မာဘာသာ: စတုဂံ

Nederlands: Vierhoek

नेपाली: चतुर्भुज

नेपाल भाषा: प्यकुं

日本語: 四角形

norsk: Firkant

norsk nynorsk: Firkant

occitan: Quadrilatèr

ଓଡ଼ିଆ: ଚତୁର୍ଭୁଜ

oʻzbekcha/ўзбекча: Toʻrtburchak

ਪੰਜਾਬੀ: ਚੁਬਾਹੀਆ

پښتو: څلورڅنډی

ភាសាខ្មែរ: ចតុកោណ

polski: Czworokąt

português: Quadrilátero

română: Patrulater

Runa Simi: Tawak'uchu

русский: Четырёхугольник

Scots: Quadrilateral

Simple English: Quadrilateral

slovenčina: Štvoruholník

slovenščina: Štirikotnik

کوردی: چوارلا

српски / srpski: Четвороугао

srpskohrvatski / српскохрватски: Četverokut

suomi: Nelikulmio

svenska: Fyrhörning

Tagalog: Kuwadrilateral

தமிழ்: நாற்கரம்

తెలుగు: చతుర్భుజి

ไทย: รูปสี่เหลี่ยม

Türkçe: Dörtgen

українська: Чотирикутник

Tiếng Việt: Tứ giác

文言: 四邊形

West-Vlams: Vieroek

吴语: 四边形

粵語: 四邊形

中文: 四邊形