1. Notes 2.1
Inductive Reasoning

2. Inductive Reasoning
Process of reasoning that a statement is true because specific cases are true.
Examples of Inductive Reasoning are:
Looking for patterns.

3. Conjecture
A statement that you believe is true by inductive reasoning.

4. Example 1: Identifying a Pattern
Find the next item in the pattern.
January, March, May, ...
(Alternating months of the year make up the pattern.)
The next month is July.

5. Example 2: Identifying a Pattern
Find the next item in the pattern.
7, 14, 21, 28, …
(Multiples of 7 make up the pattern.)
The next multiple is 35.

6. Example 3: Identifying a Pattern
Find the next item in the pattern.
In this pattern, the figure rotates 90° counter-clockwise each time.
The next figure is

7. Counterexample
An example that shows a conjecture to be false.

8. Example 4: Making Conjectures
Complete the conjecture.
The product of two odd numbers is ? .
List some examples and look for a pattern.
1  1 =  3 =  7 = 35
The product of two odd numbers is odd.

9. Inductive Reasoning
1. Look for a pattern.
2. Make a conjecture.
3. Prove the conjecture or find a counterexample.

10. Example 4: Making Conjectures
Show that the conjecture is false by finding a counterexample.
Two complementary angles are not congruent.
45° + 45° = 90°
If the two congruent angles both measure 45°, the conjecture is false.