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# Geometry Chap 2

### Vocabulary

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

Inductive Reasoning | A type of reasoning that reaches conclusions based on a pattern of specific examples or past events. |

Conjecture | A conclusion reached by using inductive reasoning |

Counterexample | An example showing that a statement is false. |

Conditional | A conditional is an if-then statment. |

Hypothesis | In an if-then statement (conditional) the hypothesis is the part that follows if. |

Conclusion | The conclusion is the part of an if-then statement (conditional) that follows then. |

Truth Value | The truth value of a statement is "true" or "false" according to whether the statement |

Negation | The negation of a statment has the opposite meaning of the original statement. |

Converse | The statement obtained by reversing the hypothesis and conclusion of a conditional. |

Inverse | The inverse of the consitional "if p, then q" is the conditional "if not p, then not q." |

Contrapositive | The contrapositive of the conditional "if p, then q" is the conditional "if not q, the not p." A conditional and its contrapositive always have the same truth value. |

Equivalent Statements | Statements with the same truth value. |

Biconditional | A biconditional statement is the combination of a conditional statement and its converse. A biconditional contains the words "if and only if." |

Deductive Reasoning | A process of reasoning logically from given facts to a conclusion. |

Law of Detachment | If the hypothesis of a true conditional is true, then the conclusion is true. |

Law of Syllogism | Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. |

Reflexive Property | A = A |

Symmetric Property | If a = b then b = a |

Transitive Property | If a = b and b = c, then a = c |

Proof | A convincing argument that uses deductive reasoning. |

Two-column proof | Lists each statement on the left. The justifcation, or the reason for each statement, is on the right. Each statement must follow logically from the steps before it. |

Theorem | Is a conjecture that is proven. |

Paragraph proof | A proof written as a paragraph. |

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