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# math ch. 8 theorems

### math ch 8 vocab... postulates... theorems

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

polygon interior Angles Theorem | the sum of the measures of the interior angles of a convex n-gon is (n-2)*180 degrees |

corollary | the sum of the measures of the interior angles of a quadrilateral is 180 degrees. |

polygon Exterior Angles Theorem | the sum of the measures of the exterior angles if a convex polygon, one angle at each vertex, is 360 degrees |

polygon Exterior Angles Theorem 2 | if a quadrilateral is a parallelogram, then its opposite sides are congruent. |

polygon Exterior Angles Theorem 3 | if a quadrilateral is a parallelogram, then its opposite angles are congruent |

polygon Exterior Angles Theorem 4 | if a quadrilateral is a parallelogram, then its diagonals bisect each other |

polygon Exterior Angles Theorem 5 | if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram,. |

polygon Exterior Angles Theorem 6 | if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |

polygon Exterior Angles Theorem 7 | if one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram |

polygon Exterior Angles Theorem 8 | of the diagonals of a quadrilateral bisect each of other then the quadrilateral is a parallelogram. |

polygon Exterior Angles Theorem 9 | if one pair of opposite sides are congruent and parallel then the quadrilateral is a parallelogram. |

Rhombus corollary | a quadrilateral is a rhombus if and only if if has four congruent sides. |

Rectangle corollary | a quadrilateral is a rectangle if and only if if has four right angles. |

square corollary | a quadrilateral is a square is and only if its a rhombus and a rectangle. |

shapes corollary | a parallelogram is a rhombus if and only if its diagonals are perpendicular. |

shapes corollary 2 | a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles. |

shapes corollary 4 | a parallelogram is a rectangles if and only if its diagonals are congruent. |

shapes corollary 5 | if a trapezoid is isosceles, then both pairs of base angles are congruent. |

shapes corollary 6 | if a trapezoid has a pair of congruent base angles, them it is an isosceles trapezoid. |

shapes corollary 7 | a trapezoid is isosceles if and only is its diagonals are congruent. |

Midsegment Theorem for trapezoids | the mud segment of a trapezoid is parallel to each bas and its length if one half the sum of the lengths of the bases. |

Midsegment Theorem for trapezoids 2 | if a quadrilateral is a kite, then exactly on pair of opposite angles are congruent. |

Midsegment Theorem for trapezoids 3 | if a quadrilateral is a kite then its diagonals are perpendicular. |

Created by:
the cat