AskDefine | Define quadrilateral

Dictionary Definition

quadrilateral adj : having four sides [syn: four-sided] n : a four-sided polygon [syn: quadrangle, tetragon]

User Contributed Dictionary

English

Etymology

From quadrilaterus (1650), quadri- (four) + latus (sided)

Noun

  1. a polygon having four sides.

Translations

polygon having four sides

Adjective

  1. having four sides.

Translations

having four sides

Extensive Definition

In geometry, a quadrilateral is a polygon with four sides or edges and four vertices or corners. Sometimes, the term quadrangle is used, for etymological symmetry with triangle, and sometimes tetragon for consistency with pentagon (5 sided), hexagon (6 sided) and so on. The interior angles of a quadrilateral add up to 360 degrees...
Quadrilaterals are either simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.

Convex quadrilaterals

Convex quadrilaterals are further classified as follows:
  • Trapezium (British English) or trapezoid (Amer.): two opposite sides are parallel.
  • Isosceles trapezium (Brit.) or isosceles trapezoid (Amer.): two opposite sides are parallel, the two other sides are of equal length, and the two ends of each parallel side have equal angles. This implies that the diagonals are of equal length.
  • Trapezium (Amer.): no sides are parallel.
  • Parallelogram: both pairs of opposite sides are parallel. This implies that opposite sides are of equal length, opposite angles are equal, and the diagonals bisect each other.
  • Kite: two adjacent sides are of equal length and the other two sides also of equal length. This implies that one set of opposite angles is equal, and that one diagonal perpendicularly bisects the other. (It is common, especially in the discussions on plane tessellations, to refer to a concave kite as a dart or arrowhead.)
  • Rhombus or rhomb: all four sides are of equal length. This implies that opposite sides are parallel, opposite angles are equal, and the diagonals perpendicularly bisect each other.
  • Rhomboid: a parallelogram in which adjacent sides are of unequal lengths and angles are oblique (not right angles).
  • Rectangle (or Oblong): all four angles are right angles. This implies that opposite sides are parallel and of equal length, and the diagonals bisect each other and are equal in length.
  • Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are equal (equiangular), with each angle a right angle. This implies that opposite sides are parallel (a square is a parallelogram), and 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.
  • Cyclic quadrilateral: the four vertices lie on a circumscribed circle.
  • Tangential quadrilateral: the four edges are tangential to an inscribed circle. Another term for a tangential polygon is inscriptible.
  • Bicentric quadrilateral: both cyclic and tangential.

More quadrilaterals

  • An geometric chevron [arrowhead] has bilateral symmetry like a kite, but the top concaves inwards.
  • A self-intersecting quadrilateral is called variously a cross-quadrilateral, butterfly quadrilateral or bow-tie quadrilateral.
  • An equiangular quadrilateral is a rectangle if convex, and an "angular eight" with corners on a rectangle if non-convex.
  • In solid geometry, a quadrilateral whose vertices do not all lie in a flat plane is a skew quadrilateral. Opposite sides in a skew quadrilateral are (segments of) skew lines.

Taxonomy

A taxonomy of quadrilaterals is illustrated by the following graph. Lower forms are special cases of higher forms. Note that "trapezium" here is referring to the British definition (the American equivalent is a trapezoid).

External links

quadrilateral in Arabic: رباعي الأضلاع
quadrilateral in Asturian: Cuadriláteru
quadrilateral in Bengali: চতুর্ভুজ
quadrilateral in Min Nan: Sì-kak-hêng
quadrilateral in Bosnian: Četverougao
quadrilateral in Bulgarian: Четириъгълник
quadrilateral in Catalan: Quadrilàter
quadrilateral in Chuvash: Тăват кĕтеслĕх
quadrilateral in Czech: Čtyřúhelník
quadrilateral in Danish: Firkant
quadrilateral in German: Viereck
quadrilateral in Modern Greek (1453-): Τετράπλευρο
quadrilateral in Spanish: Cuadrilátero
quadrilateral in Esperanto: Kvarlatero
quadrilateral in French: Quadrilatère
quadrilateral in Scottish Gaelic: Ceithir-cheàrnach
quadrilateral in Galician: Cuadrilátero
quadrilateral in Classical Chinese: 四邊形
quadrilateral in Korean: 사각형
quadrilateral in Hindi: चतुर्भुज
quadrilateral in Croatian: Četverokut
quadrilateral in Ido: Quadrilatero
quadrilateral in Italian: Quadrilatero
quadrilateral in Hebrew: מרובע
quadrilateral in Georgian: ოთხკუთხედი
quadrilateral in Kurdish: Çargoşe
quadrilateral in Latvian: Četrstūris
quadrilateral in Lithuanian: Keturkampis
quadrilateral in Limburgan: Veerhook
quadrilateral in Hungarian: Négyszög
quadrilateral in Macedonian: Четириаголник
quadrilateral in Dutch: Vierhoek
quadrilateral in Japanese: 四角形
quadrilateral in Norwegian: Firkant
quadrilateral in Polish: Czworokąt
quadrilateral in Portuguese: Quadrilátero
quadrilateral in Romanian: Patrulater
quadrilateral in Quechua: Tawak'uchu
quadrilateral in Russian: Четырёхугольник
quadrilateral in Slovenian: Štirikotnik
quadrilateral in Serbian: Четвороугао
quadrilateral in Serbo-Croatian: Četverokut
quadrilateral in Finnish: Nelikulmio
quadrilateral in Swedish: Fyrhörning
quadrilateral in Tamil: நாற்கரம்
quadrilateral in Telugu: చతుర్భుజి
quadrilateral in Thai: รูปสี่เหลี่ยม
quadrilateral in Vietnamese: Tứ giác
quadrilateral in Turkish: Dörtgen
quadrilateral in Ukrainian: Чотирикутник
quadrilateral in Vlaams: Vieroek
quadrilateral in Chinese: 四邊形

Synonyms, Antonyms and Related Words

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