# 5 Basic Theorems & 5 Basic Postulates

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## 5 Basic Postulates of Undefined Terms

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

a. Point - Existence Postulate | space contains at least four non-coplanar, noncollinear points |

b. Point - Existence Postulate | a plane contains at least three noncollinear points |

c. Point - Existence Postulate | a line contains at least two points |

Line Intersection Postulate | for any two points there is exactly one line that contains both points |

Plane Postulate | any three noncollinear points lie in exactly one plane |

Flat Plane Postulate | if two parts are contained in the plane, then the line joining these points are contained in the plane |

Plane Intersection Postulate | if two planes intersect, then their intersection is a line |

## 4 Basic Theorems of Undefined Terms

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

Line - Intersection Theorem | If two lines intersect, then their intersection is exactly one point |

Line - Plane Intersection Theorem | If a line intersects a plane not containing it then their intersection is exactly one point |

Line - Point Theorem | Given a line and a point not on the line, there is exactly one point that uses them |

Line - Plane Theorem | Given two intersecting lines, there is exactly one plane that contains the two lines |

## Basic Postulates and Theorems of Undefined Terms

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

a. Point - Existence Postulate | space contains at least four non-coplanar, noncollinear points |

b. Point - Existence Postulate | a plane contains at least three noncollinear points |

c. Point - Existence Postulate | a line contains at least two points |

Line Postulate | for any two points there is exactly one line that contains both points |

Plane Postulate | any three noncollinear points lie in exactly one plane |

Flat Plane Postulate | if two parts are contained in the plane, then the line joining these points are contained in the plane |

Plane Intersection Postulate | if two planes intersect, then their intersection is a line |

Line - Intersection Theorem | If two lines intersect, then their intersection is exactly one point |

Line - Plane Intersection Theorem | If a line intersects a plane not containing it then their intersection is exactly one point |

Line - Point Theorem | Given a line and a point not on the line, there is exactly one point that uses them |

Line - Plane Theorem | Given two intersecting lines, there is exactly one plane that contains the two lines |

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