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# ADV GEOMETRY

### Unit 5 Test 11/30

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

median | a segment joining a vertex to the midpoint of the opposite side |

centroid | the point where 3 medians of a triangle intersect |

what special properties do each median have in centroid | Big= 2/3 median Small= 1/3 median Big= 2x small Small= 1/2 big |

perpendicular bisector theorem | if a point lies on the perpendicular bisector then, it's equidistant from the endpoints of the segment |

converse of the perpendicular bisector theorem | if its equidistant from the end segments, then is a perpendicular bisector |

angle bisector theorem | the point is equidistant from the sides of the angle (segments) |

converse of the angle bisector theorem | if a point is on the interior of an angle and equidistant from the side of the angle, then the point is on the angle bisector |

circumcenter | the point where perpendicular bisectors of the side of a triangle intersect |

whats equal on the circumcenter | the non right angle segments and the sides (perpendicular bisectors) |

incenter | the point where the angle bisectors of the angles of a triangle intersect |

whats equal in the incenter | right angle segments two sides opposite from each other (think of isosocles) |

what is the circumcenter created by | perpendicular bisectors |

where is the circumcenter in acute triangles | inside |

where is the circumcenter in obtuse triangles | outside |

where is the circumcenter in right triangles | on |

what is the incenter created by | angle bisectors |

where is the incenter on triangles | always inside |

what is the centroid created by | medians |

where is the centroid on triangles | always inside |

what is the orthocenter created by | altitudes |

where is the orthocenter on acute triangles | inside |

where is the orthocenter on obtuse triangles | outside |

where is the orthocenter on right triangles | on |