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Quadrilateral
 
 
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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a quadrilateral is a polygon
Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
 with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle
Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
, and sometimes tetragon for consistency with pentagon
Pentagon

In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
 (5-sided), hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
 (6-sided) and so on. The word quadrilateral is made of the words quad and lateral. Quad means four and lateral means sides.






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all the quadrilaterals shapes with one parallel sides
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Qualrilateral with two sets of parallel sides
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What do the angels equal in an irregular quadrilateral?








Encyclopedia


In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a quadrilateral is a polygon
Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
 with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle
Triangle

A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
, and sometimes tetragon for consistency with pentagon
Pentagon

In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
 (5-sided), hexagon
Hexagon

In geometry, a hexagon is a polygon with six edges and six Vertex . A regular hexagon has Schl?fli symbol ....
 (6-sided) and so on. The word quadrilateral is made of the words quad and lateral. Quad means four and lateral means sides. The interior angles of a quadrilateral add up to 360 degrees of arc.

Quadrilaterals are either simple
Simple polygon

In geometry, a simple polygon is closed polygonal chain of line segments that do not cross each other. That is, it consists of finitely many line segments, each line segment endpoint is shared by two segments, and the segments do not otherwise intersect....
 (not self-intersecting) or complex
Complex polygon

The term complex polygon can mean two different things:*In computer graphics, as a polygon which is neither convex polygon nor concave polygon.*In geometry, as a polygon in the unitary space plane, which has two complex number dimensions....
 (self-intersecting). Simple quadrilaterals are either convex
Convex polygon

In geometry, a polygon can be either convex or concave....
 or concave.

Convex quadrilaterals

Convex quadrilaterals are further classified as follows:

  • Trapezium
    Trapezium

    The word trapezium has several meanings:* - a trapezoid .* - a quadrilateral with no parallel sides * Trapezium , a bone in the wrist* Trapezium , a group of stars in the Orion Nebula...
     (British English
    British English

    British English or UK English is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere....
    ) or trapezoid
    Trapezoid

    In geometry, a trapezoid or trapezium is a quadrilateral with twoparallel sides. The term “trapezoid” is used in North America, while the term “trapezium” is prevalent in Britain....
     (NAm.): two opposite
    Opposite

    Opposite may refer to:* Antonym, a word that means the opposite of a word* a kind of Leaf#Arrangement on the stem* Additive inverse, in mathematics, taking the negative of a number...
     sides are parallel
    Parallel (geometry)

    Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more line s or plane , or a combination of these....
    .
  • Isosceles trapezium (Brit.) or isosceles trapezoid
    Isosceles trapezoid

    An isosceles trapezoid is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides are Parallel , the two other sides are of equal length....
     (NAm.): two opposite sides are parallel and the base angle
    Angle

    In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
    s are congruent. This implies that the other two sides are of equal length, and that the diagonals are of equal length. An alternative definition is a quadrilateral with an axis of symmetry bisecting one pair of opposite sides.
  • Trapezium
    Trapezium

    The word trapezium has several meanings:* - a trapezoid .* - a quadrilateral with no parallel sides * Trapezium , a bone in the wrist* Trapezium , a group of stars in the Orion Nebula...
     (NAm.): no sides are parallel. (In British English this would be called an irregular quadrilateral, and was once called a trapezoid
    Trapezoid

    In geometry, a trapezoid or trapezium is a quadrilateral with twoparallel sides. The term “trapezoid” is used in North America, while the term “trapezium” is prevalent in Britain....
    .)
  • Parallelogram
    Parallelogram

    In geometry, a parallelogram is a quadrilateral with two sets 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 size....
    : 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. A general term including square, rectangle, rhombus and rhomboid.
  • Kite
    Kite (geometry)

    In geometry a kite, or deltoid, is a quadrilateral with two disjoint sets pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite....
    : 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
    Rhombus

    In geometry, a rhombus , or rhomb is an equilateral polygon parallelogram. In other words, it is a four-sided polygon in which every side has the same length....
     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. "A pushed-over square."
  • Rhomboid
    Rhomboid

    In geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are oblique.A shape like a circle with sides of equal length is not a rhombus....
    : a parallelogram in which adjacent sides are of unequal lengths and angles are oblique
    Oblique

    Oblique may refer to one of several things:In human anatomy,*abdominal muscles,**Abdominal external oblique muscle**Abdominal internal oblique muscle...
     (not right angles). "A pushed-over rectangle."
  • Rectangle
    Rectangle

    In geometry, a rectangle is a Closed set planar quadrilateral with four right angles. A rectangle with vertices ABCD would be denoted as .A rectangle with adjacent sides of lengths a and b has area ab and diagonals of equal length ....
     (sometimes referred to as an Oblong
    Oblong

    Oblong may refer to:*A rectangle that is not square .*Angus Oblong, American author and actor*Oblong, Illinois, a village in the United States...
    ): 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
    Square (geometry)

    In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
     (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. 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.
  • Rhombus
    Rhombus

    In geometry, a rhombus , or rhomb is an equilateral polygon parallelogram. In other words, it is a four-sided polygon in which every side has the same length....
     (four equal sides) + Rectangle
    Rectangle

    In geometry, a rectangle is a Closed set planar quadrilateral with four right angles. A rectangle with vertices ABCD would be denoted as .A rectangle with adjacent sides of lengths a and b has area ab and diagonals of equal length ....
     (four equal angles) = Square
    Square

    Square may mean:...
     (four equal sides and four equal angles) ? Parallelogram
    Parallelogram

    In geometry, a parallelogram is a quadrilateral with two sets 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 size....
     (opposite sides are parallel) ? Quadrilateral (four-sided polygon)
  • Cyclic quadrilateral
    Cyclic quadrilateral

    In geometry, a cyclic quadrilateral is a quadrilateral whose vertex all lie on a single circle. The vertices are said to be concyclic.In a cyclic quadrilateral, opposite angles are supplementary angle ....
    : the four vertices lie on a circumscribed circle.
  • Tangential quadrilateral
    Tangential quadrilateral

    In geometry, a tangential quadrilateral is a convex polygon quadrilateral whose sides all lie tangent to a single circle inscribed within the 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

  • A 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.
  • The area
    Area

    Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
     can be computed using Brahmagupta's formula
    Brahmagupta's formula

    In geometry, Brahmagupta's formula finds the area of any quadrilateral given the lengths of the sides and some of their angles. In its most common form, it yields the area of quadrilaterals that can be inscribed in a circle....
    .


Taxonomy

A taxonomy
Taxonomy

Taxonomy is the practice and science of classification. The word comes from the Greek language ', taxis and ', nomos .Taxonomies, or taxonomic schemes, are composed of taxonomic units known as taxa , or kinds of things that are arranged frequently in a hierarchical structure....
 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 North American equivalent is a trapezoid).

Quadrilateral Hierarchy

External links

  • at Geometry Atlas website.
  • and by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
  • Analytic Geometry of Quadrilaterals
  • , and of Quadrilaterals from cut-the-knot
    Cut-the-knot

    Cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variety of topics in mathematics....
  • and from Mathopenref