2.3 Apply Deductive Reasoning

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2.3 Apply Deductive Reasoning Mrs. Vazquez Geometry

g.co.1.1 ; g.co.3.9-11 Essential Question: How do you construct a logical argument? Objective: Students will be able to use deductive reasoning to form a logical argument.

Inductive reasoning uses patterns and specific examples to make a conjecture

deductive reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument

Law of detachment If the hypothesis of a conditional statement is true, then the conclusion is also true. ex) If 90o < m∡R < 180o, then ∡R is obtuse. ∡R is obtuse! 155o R

Law of Syllogism *If p, then q. *If q, then r. ♦If p, then r. If both *statements are true, then ♦statement is also true. If Jenelle gets a job, then she can afford a car. If Jenelle can afford a car, then she will drive to school. If Jenelle gets a job, then she will drive to school.

Then use deductive reasoning to show the conjecture is true. Use inductive reasoning to make a conjecture about the sum of a number and itself. Then use deductive reasoning to show the conjecture is true. 2 + 2 = 4 3 + 3 = 6 4 + 4 = 8 5 + 5 = 10 n + n = 2n The sum of a # and itself will result in twice the number.