CHAPTER 1 SECTION 2. MAKING A CONJECTURE: A conjecture is an unproven statement that is based on a pattern or observation. Much of the reasoning in geometry.

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Presentation transcript:

CHAPTER 1 SECTION 2

MAKING A CONJECTURE: A conjecture is an unproven statement that is based on a pattern or observation. Much of the reasoning in geometry consists of three 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 examples to make a general conjecture. Modify it, if necessary. ●3 Verify the Conjecture Use logical reasoning to verify that the conjecture is true in all cases. (You will do this in later chapters.)

Complete the conjecture. Conjecture: The sum of any two odd numbers is __?__. EXAMPLES: Solution:

Complete the conjecture. Conjecture: The sum of the first n odd positive integers is __?__. Solution:

Conjecture: The product of any two odd numbers is __?__. Solution:

A counterexample is an example that shows a conjecture is false. Conjecture: The sum of two numbers is always greater than the larger of the two numbers. Solution:

Conjecture: All shapes with four sides the same length are squares. Solution:

HOMEWORK HANDOUT 1.2 A& B