# Triangle

## Shape with three sides / From Wikipedia, the free encyclopedia

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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*.

**Quick Facts**Edges and vertices, Schläfli symbol ...

Triangle | |
---|---|

Edges and vertices | 3 |

Schläfli symbol | {3} (for equilateral) |

Area | various methods; see below |

Internal angle (degrees) | 60° (for equilateral) |

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 $A,$ $B,$ and $C$ is denoted $\triangle ABC.$ 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 $a$ be the length of the edge $BC,$ $b$ the length of $CA,$ and $c$ the length of $AB$; and to represent the angle measure at each corner using a Greek letter, letting $\alpha$ be the measure of angle $\angle CAB,$ $\beta$ the measure of $\angle ABC,$ and $\gamma$ the measure of $\angle BCA.$