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# Chapter 7 - Geo.

### Chapter 7 Theorems/Collaries/Postulates

Question | Answer |
---|---|

Pythagorean Theorem | in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs |

Converse of Pythagorean Theorem | if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle |

Geometric Mean (Altitude) Theorem | If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle |

45-45-90 Triangle Theorem | In a 45-45-90 triangle, the hypotenuse is the square root of 2 times as long as each leg |

30-60-90 Triangle Theorem | in a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg |

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle | |

If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle | |

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other | |

Geometric Mean (Leg) Theorem | in a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments; the length of each leg of the right triangle is the geometric mean of the lengths of hypotenuse and the segment of the hypotenuse that is |

adjacent to the leg |

Created by:
kgatling