Download presentation

Presentation is loading. Please wait.

Published byCelia Cushing Modified over 3 years ago

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, 22 26, 30 Add 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 a counterexample.

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

Similar presentations

OK

Review Examples. 1.1 Patterns and Inductive Reasoning “Our character is basically a composite of our habits. Because they are consistent, often.

Review Examples. 1.1 Patterns and Inductive Reasoning “Our character is basically a composite of our habits. Because they are consistent, often.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on digital marketing Ppt on power plant in india Ppt one hundred days of school Free ppt on employee motivation Ppt on motivation in hindi Ppt on west central railway Ppt on idiopathic thrombocytopenia purpura genetic Ppt on revolt of 1857 muslims Ppt on child labour in india free download Free ppt on components of food