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# Geometry Ch 2

### Stepp's Prentice Hall Geometry Chapter 2 Reasoning And Proof

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

conditional | another name for if, then statements |

hypothesis | the part following "if" also represented by "p" |

Conclusion | the part following "then" represented by "q" |

truth value | true or false |

converse | statement obtained by switching p and q so that q implies p |

biconditional | when a statement and its converse are both true they can be combined into one statement with "if and only if" |

Good Definitions | are reversable |

The arrow on a biconditional | points both ways |

If the converse is false | you can not write a biconditional |

the term conversely means the same as | vica versa |

deductive reasoning | logically connecting given statements to the appropriate conclusions |

Law of Detachment | if a conditional is true, then the conclusion is true any time you find the hypothesis |

Law of Syllogism | if the conclusion of one statement is also the hypothesis of another statement then you can form a third conditional statement connecting the original hypothesis with the final conclusion |

If p implies q and q implies r then | p implies r |

If p imples q is a true statement and you found p to be true then | q must be true |

If p implies q and you found q then | you know nothing you can only make a conclusion when you are given p ( unless it was an "if and only if" statement) |

iff means | if and only iff, you have a biconditional (both the statemtent AND its converse are true |

Addition Property of EQUALITY | you can add the same quanity to both sides of an equation and the result is also true |

Subtraction Property of EQUALITY | you can subtract the same quanity from both sides of an equation and the result is also true |

Multiplication Property of EQUALITY | you can multiply both sides of an equation by the same quanity and the result is also true |

Division Property of EQUALITY | you can divide both sides of an equation by the same quanity and the result is also true |

Reflexive Property of EQUALITY | everything is equal to itself (you see your reflection in a mirror) |

Symmetric Property of EQUALITY | if a = b then b=a |

Transitive Property of EQUALITY | if two things are both equal to a third thing then they are also equal to each other |

Substitution Property of EQUALITY | if a=b then you can replace a with b anywhere |

The Distributive Property | a(b + c) = ab + ac |

Properties of Congruence | Reflexive, Symmetric, and Transitive properties are not only good for equality (with numbers) they also work with congruence (figures) |

THEOREM | A statement that you can prove to be true with deductive reasoning |

Proof | the set of steps you take to show a conjecture is true |

Paragraph Proof | written statements that are backed up by proper reasons to show a stateement is true |

Two column proof | form with numberd statements and corresponding reasons for making those statements |

Given | material or information that has been supplied to you. You assume it to be true because it was "GIVEN." |

First reason in a two column proof | given |

Angle Addition Postulate | part + part = whole angle |

Last statement in a proof | the prove statement |

You have to have 2 conditionals to use the | Law of Syllogism |

Most common mistake using the Law of Detachment | assuming the converse is true |

A statemen you can prove true is a | theorem |

Vertical Angles | are opposite angles formed by two intersecting lines and they are CONGRUENT |

How do you write the two conditionals that form a biconditional | first write the if, then statement, then write it's converse |

checklist for angles | vertical, supplementary, complementary, angle addition postulate. |

Created by:
criswell216