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Geometry Section 1.1 Patterns and Inductive Reasoning

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Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. Much of the reasoning in geometry consists of three steps.

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Recognize a pattern. Make a conjecture about the pattern. A conjecture is an educated guess based on past observations. Prove the conjecture.

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Example 1: Give the next two terms in each sequence of numbers and describe the pattern in words. 2, 6, 18, 54…

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Example 1: Give the next two terms in each sequence of numbers and describe the pattern in words. 1, 3, 5, 7, 9… 10, 14, 18, 22 26, 30 Add 4

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Reasoning based on past observations is called inductive reasoning. Keep in mind that inductive reasoning does not guarantee a correct conclusion.

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Later in the course, we will prove a conjecture is true using deductive reasoning. To prove a conjecture is false, you need to show a single example where the conjecture is false. This single example is called a counterexample.

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Example 2: Show the conjecture is false. The product of two positive numbers is always greater than the larger number. If m is an integer*, then m 2 > 0. multiplication+ Positive/negative…CANT be fraction/decimal

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