Editing Rectangle (section)

{{Short description|Quadrilateral with four right angles}}
{{For|the record label|Rectangle (label)}}
{{pp|small=yes}}
{{Infobox Polygon
| name       = Rectangle
| image      = Rectangle_Geometry_Vector.svg
| caption    = Rectangle
| type       = [[quadrilateral]], [[trapezoid|trapezium]], [[parallelogram]], [[orthotope]]
| edges      = 4
| symmetry   = [[Dihedral symmetry|Dihedral]] (D<sub>2</sub>), [2], (*22), order 4
| schläfli   = {&nbsp;} × {&nbsp;}
| wythoff    =
| coxeter    = {{CDD|node_1|2|node_1}}
| area       =
| dual       = [[rhombus]]
| properties = [[convex polygon|convex]], [[isogonal figure|isogonal]], [[Cyclic polygon|cyclic]] Opposite angles and sides are congruent
}}

In [[Euclidean geometry|Euclidean plane geometry]], a '''rectangle''' is a [[Rectilinear polygon|rectilinear]] [[convex polygon]] or a [[quadrilateral]] with four [[right angle]]s. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a [[parallelogram]] containing a right angle. A rectangle with four sides of equal length is a ''[[square]]''. The term "[[wikt:oblong|oblong]]" is used to refer to a non-[[square]] rectangle.<ref name=":0">{{cite web |last=Tapson |first=Frank |date=July 1999 |title=A Miscellany of Extracts from a Dictionary of Mathematics |url=http://www.cimt.plymouth.ac.uk/resources/topics/art002.pdf |url-status=dead |archive-url=https://web.archive.org/web/20140514200449/http://www.cimt.plymouth.ac.uk/resources/topics/art002.pdf |archive-date=2014-05-14 |access-date=2013-06-20 |publisher=Oxford University Press}}</ref><ref>[http://www.mathsisfun.com/definitions/oblong.html "Definition of Oblong"]. ''Math Is Fun''. Retrieved 2011-11-13.</ref><ref>[http://www.icoachmath.com/SiteMap/Oblong.html Oblong – Geometry – Math Dictionary]. Icoachmath.com. Retrieved 2011-11-13.</ref> A rectangle with [[Vertex (geometry)|vertices]] ''ABCD'' would be denoted as {{rectanglenotation|ABCD}}.

The word rectangle comes from the [[Latin]] ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' ([[angle]]).

A '''[[#Crossed rectangles|crossed rectangle]]''' is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals<ref>{{Cite journal |doi=10.1098/rsta.1954.0003 |last1=Coxeter |first1=Harold Scott MacDonald |author1-link=Harold Scott MacDonald Coxeter |last2=Longuet-Higgins |first2=M.S. |last3=Miller |first3=J.C.P. |title=Uniform polyhedra |jstor=91532 |mr=0062446 |year=1954 |journal=Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences |issn=0080-4614 |volume=246 |pages=401–450 |issue=916 |publisher=The Royal Society|bibcode=1954RSPTA.246..401C |s2cid=202575183 }}</ref> (therefore only two sides are parallel). It is a special case of an [[antiparallelogram]], and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as [[Spherical geometry|spherical]], [[Elliptic geometry|elliptic]], and [[Hyperbolic geometry|hyperbolic]], have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.

Rectangles are involved in many [[#Tessellations|tiling]] problems, such as tiling the plane by rectangles or tiling a rectangle by [[polygon]]s.