Chapter 1 Lesson 1 Objective: To use inductive reasoning to make conjectures.

Example 1: Inductive Reasoning If you were to see dark, towering clouds approaching, you might want to take cover. Your past experience tells you that a thunderstorm is likely to happen. When you make a conclusion based on a pattern of examples or past events, you are using inductive reasoning.

Much of the reasoning you need in geometry consists of 3 stages: 1.Look for a Pattern: Look at several examples. Use diagrams and tables to help discover a pattern. 2.Make a Conjecture. Use the example to make a general conjecture. 3. Verify the conjecture. Use logical reasoning to verify the conjecture is true IN ALL CASES. (You will do this in Chapter 2 and throughout the book).

Vocabulary 1.1 Inductive ReasoningInductive Reasoning ConjectureConjecture CounterexampleCounterexample Prime NumberPrime Number investigating using the observation of patterns A conclusion reached based upon inductive observation An example that shows the conjecture is not correct A Positive number with no factors other than itself and 1. (The smallest prime number is 2.)

Example 2: Inductive Reasoning You can use inductive reasoning to find the next terms in a sequence. Find the next three terms of the sequence: 3, 6, 12, X 2 24, 48, 96, X 2

Example 3: Inductive Reasoning Mrs. Smith has given her Geometry class a pop quiz every Tuesday for the past 3 weeks. On Monday afternoon, Natalie told Beth to go home and study her Geometry notes. Why? They have a Pop Quiz on Tuesday

Example 4: Inductive Reasoning Draw the next figure in the pattern.

Example 5: Conjecture Make a conjecture about the sum of the first 30 odd numbers. Find the first few sums. Notice that each sum is a perfect square. Using inductive reasoning, you can conclude that the sum of the first 30 odd numbers is 30 2, or 900.

Example 6: Counterexample A conjecture is an educated guess. Sometimes it may be true, and other times it may be false. How do you know whether a conjecture is true or false? Try different examples to test the conjecture. If you find one example that does not follow the conjecture, then the conjecture is false. Such a false example is called a _____________. counterexample Conjecture: The sum of two numbers is always greater than either number. Is the conjecture TRUE or FALSE ? Counterexample: = is not greater than 3.

Assignment Section 1-1 Pages 6 through 8 #’s 1-11 odd 17, all all all