4 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?
5 ConjectureA conjecture is an educated guess based on known information.Examining several specific situation to arrive a conjecture is called inductive reasoning.
6 Example Lets look at the first 5 triangular numbers. 1, 3, 6, 10, 15 Find a patternConjecture: The next number will increase by 6.is 21 so 21 is the next triangular number.
7 Example Given points P, Q, and R. PQ = 9, QR = 15, and PR = 12 Conjecture: P,Q, and R are noncollinearIllustrate conjectureQ159PR12
8 CounterexampleA 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.
9 Example Given points W, X, Y, and Z Conjecture: W, X, Y, and Z are noncollinear.Counterexample:W X Y Z