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# Reasoning and Proof

### general postulates and theorems (Chp. 2)

hypothesis | conclusion |
---|---|

Through any two points | there is exactly one line |

Through any three points not on the same line | there is exactly one plane |

A line contains at least | two points |

A plane contains at least three points | not on the same line |

If two points lie in a plane | then the entire line containing those points lies in that plane |

If two lines intersect | then their intersection is exactly one point |

If two planes intersect | then their intersection is a line |

If M is the midpoint of line AB then | line AM is congruent to line MB |

The points on any line or line segment can be paired with real numbers so that given any two points A and B on a line, A corresponds to | zero, and B corresponds to a positive real number |

If B is between A and C | then AB+ BC= AC |

Congruence of segments is | reflexive, symmetric, and transitive |

Given the ray AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending | on either side of ray AB, such that the measure of the angle formed is r |

If R is in the interior of angle PQS, then the measure of angle PQR plus the measure of angle RQS equals the measure of angle PQS. If the measure of angle PQR plus the measure of angle RQS will equal the measure of angle PQS, then R is the interior of | angle PQS |

If two angles form a linear pair, then | they are supplementary angles |

If the noncommon sides of two adjacent angles form a right angle, then | the angles are complementary angles |

Congruence of angles is reflexive, symmetric, and | transitive |

Angles supplementary to the same angle or to congruent angles are | congruent |

Angles complementary to the same angle or to congruent angles are | congruent |

If two angles are verticle angles, then they are | congruent |

Perpendicular lines intersect to form four | right angles |

All right angles are | congruent |

Perpendicular lines form | congruent adjacent angles |

If two angles are congruent and supplementary, then | each angle is a right angle |

If two congruent angles form a linear pair, then | they are right angles |

Conclusion | In a conditional statement, the statement that immediately follows the word "then". |

Converse | The statement formed by exchanging the hypothesis and conclusion of a conditional statement. |

Hypothesis | In a conditional statement, the statement that immediately follows the word "if". |

Inverse | The statement formed by negating both the hypothesis and conclusion of a conditional statement. |

Created by:
m.meyer