# height

Let $ABC$ be a given triangle. A height of $ABC$ is a line segment^{} drawn from a vertex to the opposite side (or its prolongations) and perpendicular^{} to it. So we have three heights in any triangle. The three heights are always concurrent^{} and the common point is called the orthocenter^{}. In Euclidean geometry^{} the
length of the segment ”height” is sometimes referred to as the height.

In the following figure, $AD,BE$ and $CF$ are heights of $ABC$.

Title | height |
---|---|

Canonical name | Height |

Date of creation | 2013-03-22 11:55:39 |

Last modified on | 2013-03-22 11:55:39 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 15 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 51-00 |

Related topic | Triangle |

Related topic | Median |

Related topic | Orthocenter |

Related topic | Cevian |

Related topic | BaseAndHeightOfTriangle |