# Pythagorean theorem

Pythagorean theorem^{} states:

If $\mathrm{\u25b3}ABC$ is a right triangle^{}, then the http://planetmath.org/node/1087square of the length of the hypothenuse
is equal to the sum of the squares of the two legs. In the following picture, the purple squares add up to the same area as the orange one.

$$A{C}^{2}=A{B}^{2}+B{C}^{2}.$$ |

Cosines law is a generalization^{} of Pythagorean theorem for any triangle.
It implies that the converse^{} of Pythagorean theorem also holds: if
the sides of a triangle satisfy ${a}^{2}+{b}^{2}={c}^{2}$ then the triangle is a
right triangle.

Title | Pythagorean theorem |

Canonical name | PythagoreanTheorem |

Date of creation | 2013-03-22 11:43:09 |

Last modified on | 2013-03-22 11:43:09 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 28 |

Author | drini (3) |

Entry type | Theorem^{} |

Classification | msc 51-00 |

Classification | msc 20G42 |

Classification | msc 16S40 |

Classification | msc 57T05 |

Classification | msc 16W35 |

Classification | msc 81R50 |

Classification | msc 16W30 |

Synonym | Pythagoreas’ theorem |

Synonym | Pythagoras theorem |

Related topic | Triangle |

Related topic | CosinesLaw |

Related topic | Hypotenuse |

Related topic | RightTriangle |

Related topic | PythagoreanTriple |

Related topic | ProofOfPythagoreasTheorem |

Related topic | PythagorasTheorem |

Related topic | PtolemysTheorem |

Related topic | FirstPrimitivePythagoreanTriplets |

Related topic | PythagoreanTheoremInInnerProductSpaces |

Related topic | GeneralizedPythagoreanTheorem |