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# Geometry Ch. 2

### Geometric Reasoning- vocabulary

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

inductive reasoning | the process of reasoning that a rule or statement is true because specific cases are true |

conjecture | a statement believed to be true based on inductive reasoning |

counterexample | an example that proves a conjecture or statement is false |

conditional statement (words) | "if p, then q" |

hypothesis | the part p of a conditional statement following the word 'if' |

conclusion | the part q of a conditional statement following the word 'then' |

conditional statement (symbols) | p --> q |

negation of p (symbols) | ~p |

negation of p (words) | "not p" |

converse (words) | the statement formed by exchanging the hypothesis and conclusion |

converse (symbols) | q --> p |

inverse (words) | the statement formed by negating the hypothesis and the conclusion |

inverse (symbols) | ~p --> ~q |

contrapositive (words) | the statement formed by exchanging AND negating the hypothesis and conclusion |

contrapositive (symbols) | ~q --> ~p |

logically equivalent statements | statements that have the same truth value |

deductive reasoning | the process of using logic to draw conclussions |

Law of Detachment | if p-->q is true and p is true, then q is true |

Law of Syllogism | if p-->q and q-->r are true statements, then p-->r is a true statement |

biconditional statement | a statement that can be in the form "p if and only if q" |

definition | a statement that describes a mathematical object and can be written as a true biconditional statement. |

polygon | a closed plane figure formed by three or more segments such that each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear |

quadrilateral | a four sided polygon |

triangle | a three sided polygon |

proof | an argument that uses logic to show that a conclusion is true |

Addition Property of Equality | If a = b, then a + c = b + c. |

Subtraction Property of Equality | If a = b, then a - c = b - c. |

Multiplication Property of Equality | If a = b, then ac = bc. |

Division Property of Equality | If a = b, then a/c = b/c. |

Reflexive Property of Equality | a = a |

Symmetric Property of Equality | If a = b, then b = a. |

Transitive Property of Equality | If a = b and b = c, then a = c. |

Substitution Property of Equality | If a = b, then b can be substituted for a in any expression. |

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

Reflexive Property of Congruence | figure A ≅ figure A |

Symmetric Property of Congruence | If figure A ≅ figure B, then figure B ≅ figure A. |

Transitive Property of Congruence | If figure A ≅ figure B and figure B ≅ figure C, then figure A ≅ figure C. |

theorem | a statement that has been proven |

two-column proof | a style of proof in which the statements are written in the left-hand column and the reasons are written in the right-hand column |

flowchart proof | a style of proof that uses boxes and arrows to show the structure of the proof |

paragraph proof | a style of proof in which the statements and reasons are presented in paragraph form |

Created by:
rivey