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Unit 2-1 to 2-6
Pearson Geometry Unit 2
Term | Definition |
---|---|
Conjecture | a conclusion reached by using inductive reasoning; can be true or false. |
Counterexample | an example that shows that a conjecture is false. You can prove that a conjecture is false by finding one. |
Inductive reasoning | a type of reasoning that reaches conclusions based on a pattern of specific examples or past events |
Conclusion | the phrase of an if-then statement (conditional) that follows then |
Conditional | an if-then statement |
Contrapositive | reverses the order of the hypothesis and the conclusion in a conditional and negates them both |
Converse | reverses the order of the hypothesis of a conditional and the conclusion. |
Equivalent statements | statements that have the same truth value. |
Hypothesis | the phrase of an if-then statement (conditional) that follows if |
Inverse | negates both the hypothesis and the conclusion of the conditional. |
Negation | the opposite of the statement p, written as ~p, and read “not p.” |
Deductive reasoning | the process of reasoning logically from given statements or facts to a conclusion |
Law of Detachment | a law of deductive reasoning that allows you to state a conclusion is true, if the hypothesis of a true conditional is true |
Law of Syllogism | a law of deductive reasoning that allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement |
Biconditional | a single true statement that combines a true conditional and its true converse; written by joining the two parts of each conditional with the phrase if and only if. |