Chapter 1 Tools of Geometry

1. Chapter 1Tools of Geometry Sec 1 � 1 Patterns and Inductive Reasoning

2. Inductive Reasoning � Is reasoning that is based on patterns you observe. If you observe a pattern in a sequence you can use inductive reasoning to find the next term. Ex. 1: Find the next term in the sequence: A) 3, 6, 12, 24, ___, ___ B) 1, 2, 4, 7, 11, 16, 22, ___, ___ C)

3. Inductive Reasoning assumes that an observed pattern will continue. This may or may not be true. Ex: x = x � x This is true only for x = 0 and x = 1 Conjecture � A conclusion you reach using inductive reasoning.

4. Ex. 2: Make a conjecture about the sum of the first 30 odd numbers.

6. Counter Example � To a conjecture is an example for which the conjecture is incorrect. Ex.1-3: The first 3 odd prime numbers are 3, 5, 7. Make a conjecture about the 4th. 3, 5, 7, ___ One would think that the rule is add 2, but that gives us 9 for the fourth prime number. Is that true? What is the next odd prime number?

9. Homework Page 6 1-53 odd and 2,26,40,44,48

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