Chapter 2: Reasoning in Geometry

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Chapter 2: Reasoning in Geometry 2.1 Inductive Reasoning Ojectives: I CAN use patterns to make conjectures. I CAN disprove geometric conjectures using counterexamples. Geometry Chapter 2: Reasoning in Geometry

Example #1 Describe how to sketch the 4th figure. Then sketch it. Each circle is divided into twice as many equal regions as the figure number. The fourth figure should be divided into eighths and the section just above the horizontal segment on the left should be shaded. Geometry Chapter 2: Reasoning in Geometry

Example #2 Describe the pattern. Write the next three numbers. Multiply by 3 to get the next number in the sequence. Geometry Chapter 2: Reasoning in Geometry

Conjecture: conclusion made based on observation What is a conjecture? Conjecture: conclusion made based on observation What is inductive reasoning? Inductive Reasoning: conjecture based on patterns Proving conjectures TRUE is very hard. Proving conjectures FALSE is much easier. What is a counterexample? How do you disprove a conjecture? Counterexample: example that shows a conjecture is false What are the steps for inductive reasoning? How do you use inductive reasoning? Steps for Inductive Reasoning Find pattern. Make a conjecture. Test your conjecture or find a counterexample. Geometry Chapter 2: Reasoning in Geometry

Example #3 Make and test a conjecture about the sum of any 3 consecutive numbers. (Consecutive numbers are numbers that follow one after another like 3, 4, and 5.) Conjecture: The sum of any 3 consecutive numbers is 3 times the middle number. Geometry Chapter 2: Reasoning in Geometry

A counterexample was found, so the conjecture is false. Example #4 Conjecture: The sum of two numbers is always greater than the larger number. True or false? sum > larger number A counterexample was found, so the conjecture is false. Geometry Chapter 2: Reasoning in Geometry