Welcome to Geometry

1. Welcome to Geometry

2. Objective: Use inductive reasoning to make conjectures, use inductive reasoning in number/picture patterns

3. Problem Mrs. Magers has given her Geometry class a pop quiz every Tuesday for the past 3 weeks. On Monday afternoon, Natalie told Imari to go home and study her Geometry notes. Why?

4. Inductive Reasoning and Patterns • Inductive Reasoning is reasoning based on observed patterns. (We assume the observed pattern will continue. This may or may not be true.) • A conjecture is a conclusion reached through inductive reasoning. (Remember, the conjecture seems likely, but it is unproven)

5. A single counter-example is enough to disprove a conjecture. • Example Conjecture: The difference of two integers is less than either integer. • 6-4 = 2 • 10-7 =3 • Can you find a counterexample? 8-(-15) = 23

6. Given the pattern _____, -6, 12, _____, 48, … • a. Fill in the missing numbers. • b. Determine the next two numbers in this sequence. • c. Describe how you determined what numbers completed the sequence. Be sure to explain your reasoning. • d. Are there any other numbers that would complete this sequence? Explain your reasoning.

7. Ex: Find the next two terms and indicate the process for generating the next term. 1) 1, 4, 9, 16, 25, 36, ___, ___ 2) 1, 3, 7, 15, 31, 63, ___, ___ 49 64 127 255

8. 3) What figure comes next?

9. Closure • Inductive reasoning • Conjecture • Counterexample

10. homework • p.6-8 #12-30, 34-37, 43