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# Triangle Segments

### Special segments of a triangle, points of intersection, inequalities of triangle

Vocab word | Definition |
---|---|

Angle bisector | splits an angle into congruent parts |

Perpendicular bisector | splits a segment at its midpoint perpendicularly |

Median | a segment that connects a vertex of a triangle to the midpoint of the opposite side |

Altitude | a segment of a triangle that goes from a vertex perpendicularly to the opposite side |

Midsegment | a segment in a triangle that connects two midpoints |

Midpoint | a point in the middle of a segment that cuts it into two congruent parts |

Orthocenter | the point of intersection of the altitudes |

Circumcenter | the point of intersection of the perpendicular bisector |

Incenter | the point of intersection of the angle bisectors |

Centroid | the point of intersection of the medians |

Center of inscribed circle | Incenter |

Center of circumscribed circle | Circumcenter |

2/3 the distance from vertex to midpoint | Centroid |

Equidistant from the sides of a triangle | Incenter |

Equidistant from the vertices of the triangle | Circumcenter |

Triangle Inequality Theorem | Two sides of a triangle must add up to be bigger than the third side |

Largest side of a triangle | Opposite the largest angle |

Smallest side of a triangle | Opposite the smalled angle |

Largest angle of a triangle | Opposite the largest side |

Smallest angle of a triangle | Opposite the smallest side |

Hinge Theorem | If 2 sides of 2 triangles are congruent and the included angle of the first is bigger, then the third side of the first is bigger |

Hinge Theorem Converse | If 2 sides of 2 triangles are congruent and the third side of the first is bigger, then the included angle of the first is bigger |

Direct Proof | Using properties, definitions, postulates and theorems to prove something directly |

Indirect Proof | Temporarily assuming the opposite of what you are trying to prove to reach a contradiction |

Created by:
jenkroesen