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# Geometry, 5.1 - 5.3

### Midsegments, bisectors, and points of concurrency.

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

A midsegment connects the ___ of 2 sides on a ___. | midpoints; triangle |

Midsegment theorem- the midsegment of a triangle is parallel to the __ side and __ its length. | 3rd; 1/2 |

Theorem 5.2- If a point is on the perp. bisector of a segment, then it is ____ from the ___ of the segments. | equidistant; enpoints |

Theorem 5.3- If a point is equidistant from the ___ of a segment, then it is on the ____ ____ of the segment. | endpoints; perpendicular bisector |

Theorem 5.4- If a point is on the ____ of an ____, then the point is ____ from the sides of the angle. | bisector; angle; equidistant |

Theorem 5.5- If a point in the ____ of an angle is ____ from the sides of the angle, then the point is on the ____ ____. | interior; equidistant; angle bisector |

A point on the perp. bisector of a segment is | Equidistant to the endpoints |

A point on an angle bisector is | Equidistant to the sides of the angle |

Slope formula | Y2 - Y1 over X2 - X1 |

How to find a midpoint | m= (X1+X2 over 2, Y1+Y2 over 2) |

Circumcenter is formed by | Perpendicular bisectors |

A circumcenter is the | Center of the circle outside the triangle |

Incenter is formed by | Angle bisectors |

An incenter is the | Center of the circle inside the triangle |

Centroid is formed by | Medians |

A centroid is | 2/3 (2:1) the distance from vertex to midpoint |

Orthocenter is formed by | Altitudes |

An orthocenter has | No mathematical relationship |

How to find circumcenter: | Midpoint to perpendicular bisector |

How to find incenter | Vertex to side (does not have to be midpoint) |

How to find centroid | Vertex to midpoint |

How to find orthocenter | Vertex to perpendicular side, forming a right angle |

Created by:
mma129