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# Geometry 6th

### Postulates and Theorems

Term | Definition |
---|---|

Angle Bisector | Bisects an angle (cuts in half). Any point in the angle bisector is equidistant from the sides of the angle. |

Perpendicular Bisector | does not have to start at a vertex. When it Intersects the opposite side it makes a right angle (perpendicular) and bisects it. |

Altitude | Does not have to start at a vertex. When it intersects the opposite side it makes a right angle. |

Median | Does have to start at a vertex. When it intersects the opposite it bisects it. |

Midsegment | Connects two midpoints of 2 sides of a triangle. The length of the midsegment is half the 3rd side and it is parallel to the 3rd side. |

Thm. 5.2 Perpendicular Bisector Theorem | In a plane, if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. |

Thm. 5.5 Angle Bisector Theorem | If a point is on the bisector of an angle, the it is equidistant from the two sides of the angle. |

Thm. 5.10 Side to Angle Theorem | If one side of a triangle is longer than another side than the angle opposite the longer side is larger than the angle opposite the shorter side. |

Thm. 5.11 Angle to Side Theorem | If one angle is larger than another angle the side opposite the larger angle is longer than the side opposite the smaller angle. |

Thm. 5.12 Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |

Thm. 5.13 Hinge Theroem | If 2 sides of one triangle are congruent to 2 sides of another triangle,and the included angle of the 1st triangle is larger than the included angle of the 2nd triangle,then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle. |

Thm. 5.14 Converse of Hinge Theorem | If 2 sides of one triangle are congruent to 2 sides of another triangle, and the 3rd side of the 1st is longer than the 3rd side of the 2nd, then the included angle of the 1st is larger than the included angle of the 2nd. |

Created by:
daviddunham