Entry TaskComplete each sentence.

1. ? points are points that lie on the same

line.

2. ? points are points that lie in the same

plane.

3. The sum of the measures of two ? angles

is 90°.

Collinear

Coplanar

complementary

Do NOW – DISCUSS WITH YOUR TABLE

2.1Using Patterns and Inductive

Reasoning

Learning TargetI can use inductive

reasoning to make a conjecture.

inductive reasoningConjectureCounterexample

Vocabulary pg 82

Find the next item in the pattern.

Example 1: Identifying a Pattern

January, March, May, ...

The next month is July. Alternating months of the year make up the pattern.

Find the next item in the pattern.

Example 2: Identifying a Pattern

7, 14, 21, 28, …

The next multiple is 35.

Multiples of 7 make up the pattern.

Find the next item in the pattern.

Example 3: Identifying a Pattern

In this pattern, the figure rotates 90° counter-clockwise each time.

The next figure is .

When several examples form a pattern and you assume the pattern will continue, you are

applying inductive reasoning. Inductive reasoning is the process of reasoning that a

rule or statement is true because specific cases are true.

You may use inductive reasoning to draw a conclusion from a pattern. A statement you

believe to be true based on inductive reasoning is called a conjecture.

Complete the conjecture.

Example 4: Making a Conjecture

The sum of two positive numbers is ? .

The sum of two positive numbers is positive.

List some examples and look for a pattern.1 + 1 = 2 3.14 + 0.01 = 3.153,900 + 1,000,017 = 1,003,917

Check It Out! Example 5

The product of two odd numbers is ? .

Complete the conjecture.

The product of two odd numbers is odd.

List some examples and look for a pattern.1 1 = 1 3 3 = 9 5 7 = 35

Check It Out! Example 6 Make a conjecture about the lengths of male and female whales based on the data.

In 5 of the 6 pairs of numbers above the female is longer.

Female whales are longer than male whales.

Average Whale LengthsLength of Female (ft) 49 51 50 48 51 47Length of Male (ft) 47 45 44 46 48 48

To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample.

To show that a conjecture is always true, you must prove it.

A counterexample can be a drawing, a statement, or a number.

Inductive Reasoning1. Look for a pattern.2. Make a conjecture.3. Prove the conjecture or

find a counterexample.

Determine if each conjecture is true. If false, give a counterexample.

1. The quotient of two negative numbers is a positive number.

2. Every prime number is odd.

3. Two supplementary angles are not congruent.

4. The square of an odd integer is odd.

false; 2

true

false; 90° and 90°

true

HW #11

Pg 85-88 #6-30 evens #34-42 evens