Editing Triangle (section)

{{Short description|Shape with three sides}}
{{About|the basic geometric shape}}
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{{Use dmy dates|date=August 2014}}

{{Infobox Polygon
|name        = Triangle
|image       = Triangle illustration.svg
|caption     = 
|edges       = 3
|schläfli    = {3} (for equilateral)
|area        = various methods;<br>[[#Area|see below]]
}}

A '''triangle''' is a [[polygon]] with three corners and three sides, one of the basic [[shape]]s in [[geometry]]. The corners, also called [[Vertex (geometry)|''vertices'']], are zero-[[dimension]]al [[point (geometry)|points]] while the sides connecting them, also called [[Edge (geometry)|''edges'']], are one-dimensional [[line segment]]s. A triangle has three [[internal angle]]s, each one bounded by a pair of adjacent edges; the [[sum of angles of a triangle]] always equals a [[straight angle]] (180 degrees or π radians). The triangle is a [[plane figure]] and its interior is a [[planar region]]. Sometimes an arbitrary edge is chosen to be the [[base (geometry)|''base'']], in which case the opposite vertex is called the [[apex (geometry)|''apex'']]; the shortest segment between the base and apex is the [[height (triangle)|''height'']]. The [[area of a triangle]] equals one-half the product of height and base length.

In [[Euclidean geometry]], any two points determine a unique line segment situated within a unique [[straight line]], and any three points that do not [[collinearity|all lie on the same straight line]] determine a unique triangle situated within a unique flat [[plane (geometry)|plane]]. More generally, four points in [[three-dimensional Euclidean space]] determine a [[solid figure]] called ''[[tetrahedron]]''. 

In [[non-Euclidean geometry|non-Euclidean geometries]], three "straight" segments (having zero [[Geodesic curvature|curvature]]) also determine a "triangle", for instance, a [[spherical triangle]] or [[hyperbolic triangle]]. A [[geodesic triangle]] is a region of a general two-dimensional [[surface (mathematics)|surface]] enclosed by three sides that are straight relative to the surface ([[geodesic]]s). A ''{{vanchor|curvilinear}} triangle'' is a shape with three [[curve]]d sides, for instance, a ''[[circular triangle]]'' with [[circular arc|circular-arc]] sides. (This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.)

Triangles are classified into different types based on their angles and the lengths of their sides. Relations between angles and side lengths are a major focus of [[trigonometry]]. In particular, the [[trigonometric functions|sine, cosine, and tangent functions]] relate side lengths and angles in [[right triangle]]s.