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**Inductive Reasoning and Conjecture**

Chapter 1.1 and 1.2

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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 6. 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 15 9 P R 12

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Pg 5 #s evens

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Bellringer

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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 X, Y, and Z**

Conjecture: X, Y, and Z are noncollinear. Counterexample: X Y Z

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Classwork/Homework Pg 11 #s 1-19

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