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CHAPTER 1: Tools of Geometry

CHAPTER 1: Tools of Geometry. Section 1-1: Patterns and Inductive Reasoning. Objective. To use inductive reasoning to make conjectures. Vocabulary. Inductive Reasoning Conjecture Counterexample. Inductive Reasoning. Inductive reasoning is reasoning based on patters you observe.

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CHAPTER 1: Tools of Geometry

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  1. CHAPTER 1:Tools of Geometry Section 1-1: Patterns and Inductive Reasoning

  2. Objective • To use inductive reasoning to make conjectures.

  3. Vocabulary • Inductive Reasoning • Conjecture • Counterexample

  4. Inductive Reasoning • Inductive reasoning is reasoning based on patters you observe. • If you observe a pattern in a sequence, you can use inductive reasoning to predict what the next terms in the sequence will be.

  5. Finding and using a pattern • Find a pattern for each sequence. Use the pattern to show the next two terms in the sequence: • 3, 6, 12, 24……… • 1, 2, 4, 7, 11, 16………. • Ravens, Giants, Packers, Saints, Steelers………

  6. Finding and using a pattern (continued).

  7. Conjecture • A conjecture is a conclusion you reach using inductive reasoning.

  8. Using Inductive Reasoning • Make a conjecture about the sum of the first 15 odd numbers. • To get started, look at the first few sums: • 1st odd: 1 • Sum of 1st 2 odds: 1+3=4 • Sum of 1st 3 odds: 1+3+5=9 • Sum of 1st 4 odds: 1+3+5+7=16 • Do you notice anything about 1, 4, 9, and 16?

  9. Using Inductive Reasoning (continued) • The sum of the first n odds is _______. • Thus, the sum of the first 15 odds is ________. • The sum of the first 30 odds is ________.

  10. Counterexample • A counterexample to a conjecture is an example for which the conjecture is incorrect. • One counterexample proves the conjecture false.

  11. Finding a Counterexample • All prime numbers are odd. • The square of any number is greater than the number.

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