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Geometry 2.3 Big Idea: Use Deductive Reasoning

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Deductive Reasoning: logical argument. The use of facts, definitions, accepted properties and laws of logic to form a logical argument.

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Comparison Inductive: specific general Deductive: general specific

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Laws of Logic are reasonings commonly accepted to be true statements. They are used to construct a logical argument that something is true or not true.

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

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Ex.) If 2 segments have the same length, then they are congruent. Ex.) If 2 segments have the same length, then they are congruent. (True conditional statement) you are then given that Let’s say you are then given that

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Because the given information satisfies the hypothesis of the conditional statement, then it follows that the conclusion is also true:

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Law of Syllogism (sort of like transitive property) hypothesis pconclusion q If hypothesis p, then conclusion q. hypothesis qconclusion r If hypothesis q, then conclusion r. hypothesis pconclusion r If the above 2 statements are true, then the following statement is true: If hypothesis p, then conclusion r.

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Ex.1) If James takes chemistry next year, then Maria will be his lab partner. Ex.1) If James takes chemistry next year, then Maria will be his lab partner. (Assume this is true.)

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If Maria is James’ lab partner, then James will get an “A”. (Also assume this is true.)

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If James takes chemistry next year, then James will get an “A” in chemistry. (You can say this because the conclusion of the first statement is the hypothesis of the second statement which are both assumed to be true statements.)

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You have just made a logical argument using the Law of Syllogism. You created a new conditional statement that follows logically from a pair of true statements.

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Ex.2) If x > 5, then x 2 > 25. If x 2 > 25, then x 2 > 20. If x 2 > 25, then x 2 > 20. (conclusion of second statement is hypothesis of first statement) Therefore: If x > 5, then x 2 > 20.

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Identifying Inductive vs. Deductive Reasoning Inductive: if using specific examples to discover a pattern and that pattern leads you to the answer Deductive: if proving a pattern holds true for specific examples

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