Editing Quadrilateral (section)

{{Short description|Four-sided polygon}}
{{About| four-sided mathematical shapes}}
{{Redirect|Tetragon|the edible plant| Tetragonia tetragonioides}}
{{Infobox Polygon
| name          = Quadrilateral
| image         = Six Quadrilaterals.svg
| caption       = Some types of quadrilaterals
| edges         = 4
| schläfli      = {4} (for square)
| area          = various methods;<br />[[#Area of a convex quadrilateral|see below]]
| angle         = 90° (for square and rectangle)}}
In  [[Euclidean geometry|geometry]]  a '''quadrilateral''' is a four-sided [[polygon]], having four [[Edge (geometry)|edges]] (sides) and four [[Vertex (geometry)|corners]] (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a '''tetragon''', derived from Greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. [[pentagon]]). Since "gon" means "angle", it is analogously called a '''quadrangle''', or 4-angle. A quadrilateral with vertices <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> is sometimes denoted as <math>\square ABCD</math>.<ref name=":0">{{Cite web|title=Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram|url=https://www.mathsisfun.com/quadrilaterals.html|access-date=2020-09-02|website=Mathsisfun.com}}</ref>

Quadrilaterals are either [[simple polygon|simple]] (not self-intersecting), or [[complex polygon|complex]] (self-intersecting, or crossed). Simple quadrilaterals are either [[convex polygon|convex]] or [[concave polygon|concave]].

The [[Internal and external angle|interior angles]] of a simple (and [[Plane (geometry)|planar]]) quadrilateral ''ABCD'' add up to 360 [[Degree (angle)|degrees]], that is<ref name=":0" />
:<math>\angle A+\angle B+\angle C+\angle D=360^{\circ}.</math>

This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180° (here, n=4).<ref>{{Cite web|url=https://www.cuemath.com/geometry/sum-of-angles-in-a-polygon/|title=Sum of Angles in a Polygon|website=Cuemath|access-date=22 June 2022}}</ref>

All non-self-crossing quadrilaterals [[tessellation|tile the plane]], by repeated rotation around the midpoints of their edges.<ref>{{citation|last=Martin|first=George Edward|doi=10.1007/978-1-4612-5680-9|isbn=0-387-90636-3|mr=718119|at=Theorem 12.1, page 120|publisher=Springer-Verlag|series=Undergraduate Texts in Mathematics|title=Transformation geometry|url=https://books.google.com/books?id=gevlBwAAQBAJ&pg=PA120|year=1982}}</ref>