Presentation on theme: "Geometry Section 1.1 Patterns and Inductive Reasoning"— Presentation transcript:
1 Geometry Section 1.1 Patterns and Inductive Reasoning
2 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.
3 1. 2. 3. Recognize a pattern. Make a conjecture about the pattern. Recognize a pattern.Make a conjecture about the pattern.A conjecture is an educated guess based on past observations.Prove the conjecture.
4 Example 1: Give the next two terms in each sequence of numbers and describe the pattern in words. 2, 6, 18, 54…
5 Example 1: Give the next two terms in each sequence of numbers and describe the pattern in words. 1, 3, 5, 7, 9… , 14, 18, 2226, 30Add 4
6 Reasoning based on past observations is called inductive reasoning. Keep in mind that inductive reasoning does not guarantee a correct conclusion.
7 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 acounterexample.
8 Example 2: Show the conjecture is false 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 m2 > 0. multiplication+Positive/negative…CANT be fraction/decimal