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# Postulates

### Chapter 8 Quadrilaterals

Postulate/ Theorom | Definition |
---|---|

polygon interior angles theorom | the sum of the measures of the interior angles of a convex n-gon is (n-2)X 180. |

interior angles of a quad. thrm | the sum of the measures of the interior angles of a quad is 360. |

polygon exterior angles thrm. | the sum of the measures of sthe exterior angles of a convex polygon, one angle at a vertex, is 360 |

8.3 | if a quad is a parallelogram this its opp sides are congruent |

8.4 | if a quad is a parallelogram the its opp angles are congruent |

8.5 | if a quad us a parallelogram then its consecutive angles are supp |

8.6 | if a quad is a parallelogram then its diagonals bisect each other |

8.7 | if both pairs of opp sides of a quad are congruent then the quad is a parallelogram |

8.8 | if both pairs of opp angles of a quad are congruent then the quad is a parallelogram |

8.9 | if one pair of opp sides of a quad are congruent then the quad is a parallelogram |

8.10 | if the diagonals of a quad bisect each other the the quad is a parallelogram |

rhombus corollary | a quad is a rhombus if and only if it has four congruent sides |

rectangle corollary | a quad is a rectangle if and only if it has four right angles |

square corollary | a quad is a square if and only if its a rhombus and a rectgangle |

8.11 | a parallelogram us a rhombus if and only if its diagonals are perpendicular |

8.12 | a parallelogram is a rhombus if and only if each diagonal bisects a pair of opp angles |

8.13 | a parallelogram is a rectangle if and only if its diagonals are congruent |

8.14 | if a trapezoid is isosceles, then each pair of base angles are congruent |

8.15 | if a trapezoid has a pair of congruent base angles, then its an isosceles trapezoid |

8.16 | a trapezoid is isosceles if and only if its diagonals are congruent |

8.17 | the midsegment of a trapezoid is parallel to each base and its length is one half the sume of its bases |

8.18 | if a quad is a kite, then its diagonals are perpendicular |

8.19 | if a quad is a kite, then exactly one pair of opp angles ar congruent |

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