Editing Rectangle (section)

==Classification==
[[File:Symmetries_of_square.svg|280px|thumb|A rectangle is a special case of both [[parallelogram]] and [[trapezoid]]. A [[square]] is a special case of a rectangle.]]

===Traditional hierarchy===
A rectangle is a special case of a [[parallelogram]] in which each pair of adjacent [[Edge (geometry)|sides]] is [[perpendicular]].

A parallelogram is a special case of a trapezium (known as a [[trapezoid]] in North America) in which ''both'' pairs of opposite sides are [[Parallel (geometry)|parallel]] and [[equality (mathematics)|equal]] in [[length]].

A trapezium is a [[Convex polygon|convex]] [[quadrilateral]] which has at least one pair of [[parallel (geometry)|parallel]] opposite sides.

A convex quadrilateral is
* '''[[Simple polygon|Simple]]''': The boundary does not cross itself.
* '''[[Star-shaped polygon|Star-shaped]]''': The whole interior is visible from a single point, without crossing any edge.

===Alternative hierarchy===
De Villiers defines a rectangle more generally as any quadrilateral with [[Reflection symmetry|axes of symmetry]] through each pair of opposite sides.<ref>[http://mysite.mweb.co.za/residents/profmd/quadclassify.pdf An Extended Classification of Quadrilaterals] {{Webarchive|url=https://web.archive.org/web/20191230004754/http://mysite.mweb.co.za/residents/profmd/quadclassify.pdf |date=2019-12-30 }} (An excerpt from De Villiers, M. 1996. ''Some Adventures in Euclidean Geometry.'' University of Durban-Westville.)</ref>  This definition includes both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which is the [[perpendicular]] bisector of those sides, but, in the case of the crossed rectangle, the first [[axis of symmetry|axis]] is not an axis of [[symmetry]] for either side that it bisects.

Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These quadrilaterals comprise [[isosceles trapezia]] and crossed isosceles trapezia (crossed quadrilaterals with the same [[vertex arrangement]] as isosceles trapezia).