Review

Evaluate the expression for the given value of n:

3n – 2 ; n = 4 n2 – 3n ; n=6

10 and 18

Inductive Reasoning and Conjecture

GeometryUnit 9, Day 1Mr. 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:

WX

Y Z

Example

Is the following conjecture always, sometimes, or never true?

Given: Points D, E, and F are collinearConjecture: 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