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# Geometry 5th

### Postulates and theorems 5th

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

Angle Bisector | Cuts an angle in half. Any point on 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 forms a right angle and cuts the side in half. |

Median | Does have to start at a vertex. When it intersects the opposite side it cuts in half(bisects). |

Midsegment | connects two midpoints of 2 sides of a triangle. it is parallel to the third side and is half the length of the third side. |

Altitude | Does have to start at a vertex. When it intersects opposite sides it is perpendicular (makes a right angle.) |

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, then it is equidistant from the two sides of the angle. |

thm. 5.10 side to angle theorem | IF one side of the triangle is longer than another side, then the angle opposite the longersside is larger than the angle opposite. Then the angle opposite the shorter side |

thm. 5.11 angle side theorem | IF one angle of a triangle is larger than another angle, than 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 Thm | If 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angle of the first is larger that the included angle of the second, then the third side of the first is longer than the third side of the second. |

Thm. 5.14 Converse of the Hinge Thm | If 2 sides of one triangle are congruent to 2 sides of another triangle, and the third side of teh first is longer than the third side of the second, then the included angle of the first is larger than the included angles of the second |

Created by:
Thomas.lyle