# median

The *median* of a triangle is a line segment^{} joining a vertex with the midpoint^{} of the opposite side.

In the next figure, $A{A}^{\prime}$ is a median. That is, $B{A}^{\prime}={A}^{\prime}C$, or equivalently, ${A}^{\prime}$ is the midpoint of $BC$.

If the length of the three sides of the triangle are known, the length of the medians can be found by means of Apollonius theorem^{}.

Title | median |

Canonical name | Median |

Date of creation | 2013-03-22 11:44:01 |

Last modified on | 2013-03-22 11:44:01 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 18 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 51-00 |

Classification | msc 55-00 |

Classification | msc 55-01 |

Related topic | Triangle |

Related topic | ApolloniusTheorem |

Related topic | Orthocenter^{} |

Related topic | CevasTheorem |

Related topic | Centroid |

Related topic | ProofOfApolloniusTheorem2 |

Related topic | ParallelogramLaw |

Related topic | TrigonometricVersionOfCevasTheorem |

Related topic | ProofOfParallelogramLaw |

Related topic | HeightOfATriangle |

Related topic | Cevian |