# Triangle

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

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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 $\triangle ABC$.

**Quick facts: Equilateral triangle, Type, Edges and vertice...**▼

Equilateral triangle | |
---|---|

Type | Regular polygon |

Edges and vertices | 3 |

Schläfli symbol | {3} |

Coxeter–Dynkin diagrams | |

Symmetry group | Dihedral (D_{3}), order 2×3 |

Internal angle (degrees) | 60° |

Properties | Convex, cyclic, equilateral, isogonal, isotoxal |

Dual polygon | Self |

**Quick facts: Triangle, 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 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.