Geometry 2.3Geometry 2.3

Big Idea: Use Big Idea: Use Deductive Deductive ReasoningReasoning

Deductive Reasoning:

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

ComparisonInductive:

specific general

Deductive:

general specific

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 Ex.) If 2 segments have the same length, then they same length, then they are congruent. are congruent. (True conditional statement)

Let’s say you are then you are then given that given that

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

Law of SyllogismLaw of Syllogism(sort of like transitive property)

If hypothesis phypothesis p, then conclusion qconclusion q.

If hypothesis qhypothesis q, then conclusion rconclusion r.

If the above 2 statements are true, then the following statement is true: If hypothesis phypothesis p, then conclusion rconclusion r.

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

If Maria is JamesIf Maria is James’’ lab lab partner, then James will partner, then James will get an get an ““AA ””..

(Also assume this is true.)

If James takes chemistry If James takes chemistry next year, then James will next year, then James will get an get an ““AA ”” in chemistry. 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 created a new conditional statement that follows logically from a pair of true statements.

Ex.2) If x > 5, then xEx.2) If x > 5, then x22 > 25. > 25.

If xIf x22 > 25, then x > 25, then x22 > 20. > 20.

(conclusion of second statement is

hypothesis of first statement)

Therefore: If x > 5, then xTherefore: If x > 5, then x22 > 20. > 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