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# Quadrilaterals

### postulates and theorems relating to quadrilaterals (chp. 8)

hypothesis | conclusion |
---|---|

If a convex polygon has n sides and S is the sum of the measures of its interior angles | then S=180(n-2) |

If a polygon is convex | then the sum of the measures of th exterior angles, one at each vertex, is 360 |

Opposite sides of a parallelogram | are congruent |

Opposite angles of a parallelogram | are congruent |

Consecutive angles in a parallelogram | are supplementary |

If a parallelogram has one right angle | it has four right angles |

The diagonals of a parallelogram | bisect each other |

The diagonal of a parallelogram seperates the parallelogram into | two congruent triangles |

If both pairs of opposite sides of a quadrilateral are congruent | then the quaderlateral is a parallelogram |

If both pairs oppposite angles of a quadrilateral are congruent | then the quadrilateral is a parallelogram |

If the diagonals of a quadrilateral bisect each other | then the quadrilateral is a parallelogram |

If one pair of opposite sides of a quadrilateral is both parallel and congruent | then the quadrilateral is a parallelogram |

If a parallelogram is a rectangle | then the diagonals are congruent |

If the diagonals of a parallelogram are congruent | then the parallelogram is a rectangle |

The diagonals of a rhombus | are perpendicular |

If the diagonals of a parallelogram are perpendicular | then the parallelogram is a rhombus |

Each diagonal of a rhombus bisects | a pair of opposite angles |

Both pairs of base angles of an isosceles trapeziod | are congruent |

The diagonals of an isosceles trapeziod | are congruent |

The median of a trapezoid is parallel to the bases, and its measure is | one-half the sum of the measures of the bases |

Created by:
m.meyer