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# Geometry

### Postulates and Theorems

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

Angle Bisecter | bisects an angle (cuts in half). any point on the angle bisecter is equadistance from the side of the angle. |

Perpendicular Bisecter | 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 have to start at a vertex. when intersects, makes right angle |

Median | starts at vertex. when intersectes, makes right angle |

Mid-Segment | connects two midpoints of two sides of a triangle. length is half of 3rd side, and is parallel |

Thm. 5.2 Perpendicular Bisecter Theorem | in a plane, if a point is on the perpendiclar bisecter of a segment, then it is equadistant from the endpoints of the segment |

Thm. 5.5 Angle Bisecter Theorem | if a point is on the bisecter of an angle, then it is equadistant from the 2 sides of the angle |

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

Thm. 5.11 Angle to Side Theorem | if one angle is larger than another, then 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 legths of any two sides of a triangle is greater than the length of the third side |

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

Thm. 5.14 Converse of the Hinge Thm. | If 2 sides of 1 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:
laurengrawunder