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Bellringer Find the circumference and area of the circle. 4/3 cm

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Edmodo Homework grade for signing up for class on edmodo –Group Code: lw9hra

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Inductive Reasoning and Conjecture Chapter 2-1

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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?

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

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

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Homework Pg 63 #s 1-18, Edmodo –Group Code: lw9hra

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