Review Evaluate the expression for the given value of n: 3n – 2 ; n = 4 n 2 – 3n ; n=6 10 and 18

Inductive Reasoning and Conjecture Geometry Unit 9, Day 1 Mr. Zampetti

Objective To learn how to make conjectures based on inductive reasoning To find counterexamples of conjectures

Definition Conjecture: an educated guess based on known information. Example Given: 2, 4, 6, 8 Conjecture: The next number will be 10

Definition Inductive Reasoning: reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction You use inductive reasoning to find conjectures

Make a conjecture Given: 1, 3, 6, 10, 15 find the next number Conjecture: The next number will be 21.

Counterexample A counterexample is a false example to show a conjecture to be not true

Find a counterexample: Given: points W, X, Y, Z Conjecture: W, X, Y, and Z are noncollinear Counterexample: W X Y Z

Example Is the following conjecture always, sometimes, or never true? Given: Points D, E, and F are collinear Conjecture: DE + EF = DF Sometimes!!

With a partner: Make a conjecture about the next item in the sequence: -8, -5, -2, 1, 4 Determine whether each conjecture is true or false. Give a counterexample for a false conjecture: Given: x is an integer. Conjecture: -x is negative.

With a partner (cont.): Determine whether each conjecture is true or false. Give a counterexample for a false conjecture: Given: WXYZ is a rectangle Conjecture: WX = YZ and WZ = XY

With a partner (cont.): Most homes in the northern United State have roofs made with steep angles. In the warmer areas of the southern states, homes often have flat roofs. Make a conjecture about why the roofs are different.

Homework Work Packet: Inductive Reasoning and Conjecture