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# geometry chapter 5

### conjectures from chapter 5

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

quadrilater sum conjecture | The sum of the measures of the four angles of any quadrilateral is 360 |

Pentagon Sum Conjecture | The sum of the measures of the five angles of any pentagon is 540°. |

Polygon Sum Conjecture | The sum of the measures of the n interior angles of an n-gon is (n−2)•180. |

Exterior Angle Sum Conjecture | For any polygon, the sum of the measures of a set of exterior angles is 360°. |

Equiangular Polygon Conjecture | You can find the measure of each interior angle of an equiangular n- gon by using either of these formulas: (n−2)•180 ° n or 180 -360 ° n |

Kite Angles Conjecture | The non-vertex angles of a kite are congruent |

Kite Diagonals Conjecture | The diagonals of a kite are perpendicular. |

Kite Diagonal Bisector Conjecture | The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal. |

Kite Angle Bisector Conjecture | The vertex angles of a kite are bisected by a diagonal. |

Trapezoid Consecutive Angles Conjecture | The consecutive angles between the bases of a trapezoid are supplementary. |

Isosceles Trapezoid Conjecture | The base angles of an isosceles trapezoid are congruent. |

Isosceles Trapezoid Diagonals Conjecture | The diagonals of an isosceles trapezoid are congruent |

Three Midsegments Conjecture | The three midsegments of a triangle divide it into four congruent triangles. |

Triangle Midsegment Conjecture | A midsegment of a triangle is parallel to the third side and half the length of the third side. |

Trapezoid Midsegment Conjecture | The midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the lengths of the bases. |

Parallelogram Opposite Angles Conjecture | The opposite angles of a parallelogram are congruent |

Parallelogram Consecutive Angles Conjecture | The consecutive angles of a parallelogram are supplementary. |

Parallelogram Opposite Sides Conjecture | The opposite sides of a parallelogram are congruent. |

Parallelogram Diagonals Conjecture | The diagonals of a parallelogram bisect each other. |

Double-Edged Straightedge Conjecture | If two parallel lines are intersected by a second pair of parallel lines that are the same distance apart as the first pair, then the parallelogram formed is a rhombus. |

Rhombus Diagonals Conjecture | The diagonals of a rhombus are perpendicular and they bisect each other. |

Rhombus Angles Conjecture | The diagonals of a rhombus bisect the angles of the rhombus. |

Rectangle Diagonals Conjecture | The diagonals of a rectangle are congruent and bisect each other. |

Square Diagonals Conjecture | The diagonals of a square are congruent, perpendicular,and bisect each other. |

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