Editing Rectangle (section)

==Characterizations==
A [[Convex polygon|convex]] [[quadrilateral]] is a rectangle [[if and only if]] it is any one of the following:<ref>Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, pp. 34–36 {{isbn|1-59311-695-0}}.
</ref><ref>{{cite book |author1=Owen Byer |author2=Felix Lazebnik |author3=Deirdre L. Smeltzer|author3-link=Deirdre Smeltzer |title=Methods for Euclidean Geometry |url=https://books.google.com/books?id=W4acIu4qZvoC&pg=PA53 |access-date=2011-11-13 |date=19 August 2010 |publisher=MAA |isbn=978-0-88385-763-2 |pages=53–}}</ref>
* a [[parallelogram]] with at least one [[right angle]]
* a parallelogram with [[diagonal]]s of equal length
* a parallelogram ''ABCD'' where [[triangle]]s ''ABD'' and ''DCA'' are [[Congruence (geometry)|congruent]]
* an equiangular quadrilateral
* a quadrilateral with four right angles
* a quadrilateral where the two diagonals are equal in length and [[Bisection|bisect]] each other<ref>Gerard Venema, "Exploring Advanced Euclidean Geometry with GeoGebra", MAA, 2013, p. 56.</ref>
* a convex quadrilateral with successive sides ''a'', ''b'', ''c'', ''d'' whose area is <math>\tfrac{1}{4}(a+c)(b+d)</math>.<ref name=Josefsson/>{{rp|fn.1}}
* a convex quadrilateral with successive sides ''a'', ''b'', ''c'', ''d'' whose area is <math>\tfrac{1}{2} \sqrt{(a^2+c^2)(b^2+d^2)}.</math><ref name=Josefsson>{{cite journal | author = Josefsson Martin | year = 2013 | title = Five Proofs of an Area Characterization of Rectangles | url = http://forumgeom.fau.edu/FG2013volume13/FG201304.pdf | journal = Forum Geometricorum | volume = 13 | pages = 17–21 | access-date = 2013-02-08 | archive-date = 2016-03-04 | archive-url = https://web.archive.org/web/20160304001152/http://forumgeom.fau.edu/FG2013volume13/FG201304.pdf | url-status = dead }}</ref>