Notes 2.1 Inductive Reasoning.

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Presentation transcript:

Notes 2.1 Inductive Reasoning

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

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

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.

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.

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 .

Counterexample An example that shows a conjecture to be false.

Example 4: Making Conjectures Complete the conjecture. The product of two odd numbers is ? . List some examples and look for a pattern. 1  1 = 1 3  3 = 9 5  7 = 35 The product of two odd numbers is odd.

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

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.