Geometry 2.3 Big Idea: Use Deductive Reasoning

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

Comparison Inductive: specific general Deductive: general specific

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.

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

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

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

(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.

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

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.)

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.)

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.

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.

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