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# Postulates -Theorems

### Geometry postulates and theorems

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

Postulate 5 | Through any two points there exists exactly one line |

Postulate 6 | Through any three noncollinear points there exists exactly one plane |

Theorem 4-1 | If two lines intersect, then they intersect at exactly one point |

Theorem 4-2 | If there is a line and a point not on the line, then exactly one plane contains them |

Theorem 4-3 | If two lines intersect, then there exists exactly one plane that contains them |

Postulate 7 | If two planes intersect, then their intersection is a line. |

Postulate 8 | If two points lie on a plane, then the line containing them lies in the plane |

Postulate 9 | A line contains at least 2 points. A plane contains at least three noncollinear points. Space contains at least 4 noncoplanar points |

Theorem 5-2 | If two lines in a plane are perpendicular to the same line, then they are parallel to each other |

Theorem 5-3 | In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other one. |

Theorem 5-1 | If two parallel planes are intersected by a third plane,then the lines of intersection are parallel |

Theorem 5-4 | If two lines are perpendicular, then they form congruent adjacent angles |

Theorem 5-5 | If two lines form congruent adjacent angles, then they are perpendicular |

Theorem 5-6 | All right angles are congruent |

Postulate 10: The Parallel Postulate | Through a point not on a line, there exists exactly one line through the point that is parallel to the line |

Theorem 5-7: Transitive Property of Parallel Lines | If two lines are parallel to the same line, then they are parallel to one another |

Created by:
ojw1230