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# geometry c

### postulates, theorems, definitions

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

Theorem 1.1 | if two distinct lines intersect, then they intersect at exactly one point |

Theorem 1.2 | if there is a line and a point not on the line, then there is exactly one plane that contains them |

Theorem 1.3 | if two distinct lines intersect, then they lie in exactly one plane |

Theorem 1.4 | each segment has exactly 1 midpoint |

Theorem 1.5 | midpoint theorem- if m is the midpoint of a segment of line AB, then: 2AM=AB and AM=1/2AB..... and 2MB=AB and MB=1/2AB |

Theorem 1.6 | in a half plane, through the end point of a ray lying in the edge of a half-plane, there is exactly one other ray such that the angle formed by the two rays has given measure between 0 and 180 |

Theorem 1.7 | all right angles are congruent |

Theorem 1.8 | angle bisector theorem: if ray OX is the bisector of <AOB, then: 2m<AOX= m<AOB and m<AOX= 1/2m<AOB... and 2m<XOB= m<AOB and m<XOB= 1/2m<AOB |

Theorem 1.9 | if 2 angles are vertical, then they are congruent |

Theorem 1.10 | if 2 lines are perpendicular, then the pairs of adjacent angles they form are congruent |

Theorem 1.11 | if 2 lines intersect to form a pair of congruent adjacent angles, then the lines are perpendicular |

Theorem 1.12 | if there is given any point on a line in a plane, then there is exactly one line in that plane perpendicular to the given line at the given point |

Theorem 1.13 | if the exterior sides of 2 adjacent acute angles are perpendicular, then the angles are complementary |

Theorem 1.14 | if there is a point not on the line, then there is exactly one line perpendicular to the given line through the given point |

Theorem 2.1 | congruence of segments is reflexive, symmetric, and transtive |

Theorem 2.2 | congruence of angles is reflexive, symmetric, and transtive |

Theorem 2.3 | if 2 angles are supplements of congruent angles or of the same angles, then the 2 angles are congruent |

Theorem 2.4 | if 2 angles are complements of congruent angles |

Theorem 3.1 | if 2 parallel lines are intersected by a third plane, then the lines of intersection are parallel |

Theorem 3.2 | if parallel lines have a transversal, then alternate interior angles are congruent |

Theorem 3.3 | if parallel lines have a transversal, then alternate exterior angles are congruent |

Theorem 3.4 | if parallel lines have a transversal, then interior angles on the same side of the transversal are supplementary |

Theorem 3.5 | if a transversal intersecting 2 parallel lines is perpendicular to one of the lines, it is also perpendicular to the other line |

Theorem 3.6 |

Created by:
kiran_basra2