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# geo relations in tri

### relationships and inequalities in triangles (chp. 5)

hypothesis | conclusion |
---|---|

Any point on the perpendicular bisector of a segment... | is equidistant from the endpoints of the segment. |

Any point equidistant from the endpoints of a segment... | lies on the perpendicular bisector of the segment. |

The circumcenter of a triangle... | is equidistant from the vertices of the triangle. |

Any point on the angle bisector... | is equidistant from the sides of the angle. |

The incenter of a triangle... | is equidistant from each side of the triangle. |

The centroid of a triangle is located... | 2/3 of the distance from a vertex to the midpoint of the opposite side. |

If an angle is an exterior angle of a triangle... | then its measure is greater than the measure of either remote interior angle. |

If one side of a triangle is longer than another side,... | then the angle opposite the longer side has a greater measure that the angle opposite the shorter side. |

If one angle of a triangle has a greater measure than another angle... | then the side opposite the angle with a greater measure is longer than the side opposite the lesser angle. |

The sum of the lengths of any two sides of a triangle... | is greater than the length of the third side. |

The perpendicular segment from a point to a line... | is the shortest segment from the point to the line. |

The perpendicular segment from a point to a plane... | is the shortest segment from the point to the plane. |

(SAS inequality) If two sides of a triangle are congruent to sides of another triangle and the included angle in one triangle has a greater measure than the included side of another triangle... | then the third side of the first triangle is longer than the third side of the second triangle. |

(SSS inequality) If two sides of a triangle are congruent are congruent to sides of another triangle and the third side in one triangle is longer than the third side of the other,... | then the angle between the pair of congruent sides in the first triangle is greater than the angle between the congruent sides in the second triangle. |

Created by:
m.meyer