# Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ${\displaystyle \triangle ABC}$.[1]

Equilateral triangle
A regular triangle
TypeRegular polygon
Edges and vertices3
Schläfli symbol{3}
Coxeter diagram
Symmetry groupDihedral (D3), order 2×3
Internal angle (degrees)60°
Dual polygonSelf
PropertiesConvex, cyclic, equilateral, isogonal, isotoxal
Triangle
A triangle
Edges and vertices3
Schläfli symbol{3} (for equilateral)
Areavarious methods;
see below
Internal angle (degrees)60° (for equilateral)

In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.