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Quadrilateral ○꠹｜Definition｜1st｜20260419155516-00-⌔

Quadrilateral - Wikipedia

Quadrilateral

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In geometry, a quadrilateral is a four-sided polygon, having four edges (sides) and four 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 $A$, $B$, $C$ and $D$ is sometimes denoted as $\square ABCD$.¹

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

The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees, that is¹

• ✤ $\angle A+\angle B+\angle C+\angle D=360^{\circ }.$

This is a special case of the n -gon interior angle sum formula: S = (n − 2) × 180° (here, n=4).²

All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges.³

Printed 2026-06-28.

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Footnotes

1. “Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid, Parallelogram”. Mathsisfun.com. Retrieved 2020-09-02. ↩ ↩²

2. “Sum of Angles in a Polygon”. Cuemath. Retrieved 22 June 2022. ↩

3. Martin, George Edward (1982), Transformation geometry, Undergraduate Texts in Mathematics, Springer-Verlag, Theorem 12.1, page 120, doi:10.1007/978-1-4612-5680-9, ISBN 0-387-90636-3, MR 0718119 ↩

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