Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the.

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Presentation transcript:

Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the biconditional forms: Converse: Inverse: Contrapositive: Biconditional :

Inductive and Deductive Reasoning Chapter 2.2

Conjectures and Inductive Reasoning https://study.com/academy/lesson/inductive-and-deductive-reasoning-in-geometry.html (Topic video) Conjecture: an unproven statement that is based on observations Inductive Reasoning: what you use when you find a pattern in a specific case and then make a conjecture for the general case (like the brown mice).

Inductive Reasoning and Counterexamples Counterexample: a specific case for which the conjecture is false. To show that a conjecture is true, it must be true for ALL cases! Example of a counterexample: conjecture: The sum of two numbers is always more than the bigger number. 4+5 = 9 This would make the conjecture true because 9 > 5 This is a counterexample -4+(-5) = -9 The conjecture is false because -9 is NOT greater than -4

Deductive Reasoning Deductive Reasoning: uses facts and the laws of logic to form an argument. There are 2 laws of logic: 1) Law of Detachment: If a conditional statement is true, and the hypothesis (p) is true, then the conclusion (q) must also be true. True statement! Example: If I miss my bus, I will be late to school. p is true I missed my bus. therefore….. q is true I will be late to school.

Inductive and Deductive Reasoning https://study.com/academy/lesson/law-of-syllogism-in-geometry-definition-examples.html (Topic video) Law of Syllogism: It’s like the transitive property of equality in algebra: if A=B and B=C then A=C If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If hypothesis p, then conclusion r. If these statements are true, Then this statement is true. Example If I get to the Café late, then I will not have time to eat lunch. If I do not have time to eat lunch then I will be hungry. If I get to the Café late, then I will be hungry.