This article is about the basic geometric shape. For other uses, see Triangle (disambiguation).
"Triagonal" redirects here. For diagonals of three-dimensional shapes, see Space diagonal.
Triangle
A triangle
Edges and vertices
3
Schläfli symbol
{3} (for equilateral)
Area
various methods; see below
Internal angle (degrees)
60° (for equilateral)
Triangle = Tri (three) + Angle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. The triangle's interior is a two-dimensional region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex.
In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points, when non-collinear, determine a unique triangle situated within a unique flat plane. More generally, several points in Euclidean space of arbitrary dimension determine a simplex.
In non-Euclidean geometries three straight segments also determine a triangle, for instance a spherical triangle or hyperbolic triangle. A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides which are straight relative to the surface. A curvilinear triangle is a shape with three curved sides, for instance a circular triangle with circular-arc sides. This article is about straight-sided triangles in Euclidean geometry, except where otherwise noted.
A triangle with vertices and is denoted In describing metrical relations within a triangle, it is common to represent the length of the edge opposite each vertex using a lower-case letter, letting be the length of the edge the length of and the length of ; and to represent the angle measure at each corner using a Greek letter, letting be the measure of angle the measure of and the measure of
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