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# geometry

### math stuff

Term | Definition |
---|---|

what is the Circumcenter? | It is equidistant from the three vertices |

how do you find the circumcenter? | Bisect the three sides, the place where they all meet is the circumcenter |

what is the incenter? | Equidistant from the sides of the triangle |

how do you find the incenter? | BIsect the tree angles, the place where they all meet is the incenter |

what is the orthocenter? | where the three altitudes intersect |

how do you find the orthocenter? | find the three altitudes |

on an acute triangle where is the circumcenter? | inside |

on an obtuse triangle where is the circumcenter? | outside |

on a right triangle where is the circumcenter? | on the hypotenuse |

on any triangle where is the incenter? | it is always in the inside |

what is the median? | a line segment from the vertex to the midpoint of the opposite side |

what is the centroid? | where the three medians intersect |

how do you find the centroid? | x1+x2+x3 , y1+y2+y3 ̅ ̅ ̅ ̅ ̅ ̅ ̅3 ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅3 ̅ ̅ ̅ ̅ ̅ ̅ ̅ |

what is altitude? | a perpendicular line segment from one side to the opposite vertex |

where are the altitudes on an acute triangle? | all inside |

where are the altitudes on an obtuse triangle? | 1 inside, 2 outside |

where are the altitudes on a right triangle? | 1 inside, 2 on the legs |

a² + b² > c² What kind of triangle is this? | acute |

a² + b² < c² What kind of triangle is this? | obtuse |

a² + b² = c² What kind of triangle is this? | right |

On a 45,45,90 triangle you are given one of the legs (X) how do you find the hypotenuse? | X√2 |

On a 45,45,90 triangle you are given the hypotenuse (X) how do you find the legs? | X√2/2 (x rad 2 over 2) |

On a 30,60,90 triangle you are given the short leg (x), how do you find the long leg and hypotenuse? | Long: X√3 .......... Hypotenuse: 2X |

On a 30,60,90 triangle you are given the hypotenuse (X), how do you find the long and short legs? | Short: X/2 ............. Long: X√3 /2 |

On a 30,60,90 triangle you are given the long leg (X), how do you find the short leg and hypotenuse? | Short: X√3/3 ........... Long: 2X√3/3 |

Created by:
cosettegiroux