Download 2.1 Use Inductive Reasoning

Geometry Chapter 2: Reasoning and Proof Section 2.1-­‐ Use Inductive Reasoning SWBAT: describe patterns and use inductive reasoning. Common Core: •
G.CO.9. Prove theorems about lines and angles. Vocabulary: conjecture, inductive reasoning, and counterexample Example 1: Describe a visual pattern Example 2: Describe a number pattern Describe the pattern in the numbers 1000, 500, 250, 125, … and write the next three numbers in the pattern. Geometry Chapter 2: Reasoning and Proof Example 3: Make a Conjecture Given the pattern of triangles below, make a conjecture about the number of segments in a similar diagram of 5 triangles. Example 4: Make and test a Conjecture Numbers such as 3, 11, 15, and 29 are odd numbers. Make and test conjecture about the product of any two odd numbers. v Disproving Conjectures: To show that a conjecture is true, you must show that it is true for all cases. However, you can show that a conjecture is false by finding one case where the conjecture doesn’t work. A ______________________________________________ is a specific case for which the conjecture is false. Geometry Chapter 2: Reasoning and Proof Example 5: Find a counterexample to disprove the conjecture: Supplementary angles are always adjacent. Example 6: Standardized Test Practice Homework: Handout 2.1 Practice B