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

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Presentation transcript:

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

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

Inductive Reasoning and Conjecture Chapter 2-1

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?

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

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. 15 + 6 is 21 so 21 is the next triangular number.

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

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.

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

Homework Pg 63 #s 1-18, 29-36 Edmodo Group Code: lw9hra