Sec 2-1

Concept: Use Inductive ReasoningObjectives: Given a pattern, describe it through inductive reasoning

Example 1:

Example 2:

Example 3: Find the next number in the pattern

1. 17,15,12,8,…..____ = 3

2. 7,7.5,8, 8.5,….____ = 9

3 Stages of Inductive Reasoning in Geometry

1. Look for a pattern

2. Make a conjecture A Conjecture is an unproven

statement that is based on observations.

3. Verify the conjecture

Example 4: Sketch the next figure in the pattern

1.

2.

Example 5: Complete the conjecture based on the pattern you observe

1. The sum of any two odd numbers is ____ EVEN

Try some examples to see a pattern:

9+3

11+5

-3+-1

-7+3

Example 6: Write a function rule relating x and y.

Example 7: Show the conjecture is false by finding a counterexample

A counterexample is an example that shows a conjecture is false.

1. If the product of two numbers is positive, then the two numbers must both be positive

False: a negative number multiplied by another negative number is a positive number

Today’s Work