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Inductive Reasoning and Conjecture Chapter 1.1 and 1.2.

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Presentation on theme: "Inductive Reasoning and Conjecture Chapter 1.1 and 1.2."— Presentation transcript:

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2 Inductive Reasoning and Conjecture Chapter 1.1 and 1.2

3 How can inductive reasoning help predict weather conditions? What are normal temperatures for the month of August? How do people benefit from the inductive reasoning techniques of meteorologists?

4 Conjecture A conjecture is an educated guess based on known information. Examining several specific situation to arrive a conjecture is called inductive reasoning.

5 Example Lets look at the first 5 triangular numbers. 1, 3, 6, 10, 15 Find a pattern Conjecture: The next number will increase by is 21 so 21 is the next triangular number.

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7 Example Given points P, Q, and R. PQ = 9, QR = 15, and PR = 12 Conjecture: P,Q, and R are noncollinear Illustrate conjecture Q PR

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9 Pg 5 #s evens

10 Bellringer

11 Counterexample A conjecture based on several observations may be true in most circumstances, but false in others. It takes only one false example to show a conjecture is not true. The false example is called a counterexample.

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13 Example Given points X, Y, and Z Conjecture: X, Y, and Z are noncollinear. Counterexample: X Y Z

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16 Classwork/Homework Pg 11 #s 1-19


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