1. 2.1 Inductive Reasoning Objectives:
I CAN use patterns to make conjectures.
I CAN disprove geometric conjectures using counterexamples.

2. Example #1 Describe how to sketch the 4th figure. Then sketch it.
Each circle is divided into twice as many equal regions as the figure number. The fourth figure should be divided into eighths and the section just above the horizontal segment on the left should be shaded.

3. Example #2 Describe the pattern. Write the next three numbers.
Multiply by 3 to get the next number in the sequence.

4. What comes next? (look @ notes)
How do we know what comes next?

5. Conjecture: conclusion made based on observation
What is a conjecture?
Inductive Reasoning: conjecture based on patterns
What is inductive reasoning?
Proving conjectures TRUE
is very hard.
Proving conjectures FALSE
is much easier.
Write in your foldable
What is a counterexample?
How do you disprove a conjecture?
Counterexample: example that shows a conjecture is false
What are the steps for inductive reasoning?
How do you use inductive reasoning?
Steps for Inductive Reasoning
Find pattern.
Make a conjecture.
Test your conjecture or find a counterexample.

6. Inductive Reasoning Look @ notes

7. The sum of any 3 consecutive numbers is 3 times the middle number.
Example #3 Make and test a conjecture about the sum of any 3 consecutive numbers. (Consecutive numbers are numbers that follow one after another like 3, 4, and 5.)
Conjecture:
The sum of any 3 consecutive numbers is 3 times the middle number.

8. Counterexample Look @ notes

9. A counterexample was found, so the conjecture is false.
Example #4 Conjecture: The sum of two numbers is always greater than the larger number. True or false?
sum > larger number
A counterexample was found, so the conjecture is false.
Serra - Discovering Geometry
Chapter 2: Reasoning in Geometry

10. Examples
1. Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure.

11. Example