Presentation on theme: "Bellringer Find the circumference and area of the circle. 4/3 cm."— 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 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 PR
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