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Definitions

A quadrilateral (also called a tegragon or quadrangle) is a figure made up of four coplanar segments that have four non-colinear points as their endpoints and that intersect only at those four points.

non-quadrilateral 1 non-quadrilateral 1 quadrilateral 1
Not a quadrilateral because three of the points (A, C and D) are colinear. Not a quadrilateral because two of the segments, segment AD and segment BE, intersect at a point other than their endpoints. This is a quadrilateral.

Two sides of a quadrilateral that have a common end point are called consecutive sides. Two sides of a quadrilateral that don't have a common end point are called opposite sides. The segment that connects a pair of opposite vertices is called a diagonal.

In the right hand figure above we have the following examples:

Segment Type Examples
opposite sides segment AB and segment CD, segment BC and segment AD
consecutive sides segment AB and segment BC, segment BC and segment CD, segment CD and segment AD, segment AD and segment AB
diagonals segment AC and segment BD (not drawn in the figure)

Special Quadrilaterals

Name Description Example
trapezoid a quadrilateral where exactly one pair of sides are parallel trapezoid
isosceles trapezoid a trapezoid where the non-parallel sides are congruent isoseles trapezoid
parallelogram a quadrilateral where both pairs of opposite sides are parallel parallelogram
rectangle a qudrilateral where all of the angles are right angles rectangle
square a quadrilateral where all of the angles are right angles and all of the sides are congruent square
rhombus a quadrilateral where all of the sides are congruent rhombus
kite a quadrilateral where one pair of consecutive sides are congruent and the remaining two sides are congruent but the sides in the two pairs are not congruent kite