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# Chapter 5

### Relationships within Triangles

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

Midpoint Formula | (x1+x2/2,y1+y2/2) |

Distance Formula | Square Root of 9(x1-x2)2+(y1-y2)2 |

Slope Formula | y2-y1/x2-x1 |

Midsegment Theorem | the midsegment of a triangle is parallel to the third side and is half as long as the third side |

Perpendicular Bisector Theorem | in a plane, if a point is on the perpendicular bisector of a segment, the the point is equidstant from the end points of the segment |

Converse of the Perpendicular Bisector Theorem | in a plane, if a point is equidstant from the end points of the segment, then the point is on the perpendicular bisector of a segment |

Angle Bisector Theorem | if a point on the bisector of an angle, then the perpendicular segments from the point to each ray |

Converse Angle Bisector Theorem | if a point is in the interior of an angle and the perpendicular segments from the point to each ray are equidstant, then it lies on the bisector of the angle |

Incenter of a Triangle Theorem | the incenter of a triangle is equidstant from the sides od the triangle |

Concurrency of Medians of a Triangle Theorem | the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side |

Parts of an Isosceles Triangle | in an isoscels triangle, if an altitude, median, perpendicular bisector, and angle bisector comes from the vertex angle, then that segment is also an altitude, median, perpendicular bisector, and angle bisector. |

Side Theorem | if 1 side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side |

Angle Theorem | if 1 angle of a triangle is longer than another angle, then the side opposite the larger angel is longer than the side opposite the smaller angle |

Triangle Inequality Theorem | the sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side |

Hinge Theorem | if 2 sides of 1 triangle are congruent to 2 sides of another triangle and the included angle of the 1st is larger than the included angle of the 2nd, then the 3rd side of the 1st is longer than the 3rd side of the 2nd |

Converse of the Hinge Theorem | 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:
nhpride