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**Geometry 2.3 Big Idea: Use Deductive Reasoning**

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Deductive Reasoning: 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**

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) 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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**(sort of like transitive property)**

Law of Syllogism (sort of like transitive property) If hypothesis p, then conclusion q. If hypothesis q, then conclusion 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. (Assume this is true.)**

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**If Maria is James’ lab partner, then James will get an “A”**

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 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 x2 > 25. If x2 > 25, then x2 > 20**

Ex.2) If x > 5, then x2 > 25. If x2 > 25, then x2 > 20. (conclusion of second statement is hypothesis of first statement) Therefore: If x > 5, then x2 > 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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