4How 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?
5ConjectureA conjecture is an educated guess based on known information.Examining several specific situation to arrive a conjecture is called inductive reasoning.
6Example 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.
7Example Given points P, Q, and R. PQ = 9, QR = 15, and PR = 12 Conjecture: P,Q, and R are noncollinearIllustrate conjectureQ159PR12
8CounterexampleA 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.
9Example Given points W, X, Y, and Z Conjecture: W, X, Y, and Z are noncollinear.Counterexample:W X Y Z