Chapter 2 Reasoning and Proof

2.1 Inductive Reasoning and Conjecture Conjecture: an educated guess based on known information. Inductive reasoning: reasoning that uses a number of specific examples to arrive at a plausible generalization or prediction. Example #1: Make a conjecture about the next term in the sequence below. 20, 16, 11, 5, -2, -10 Answer: -19 (each number is reduced by one more: 20-4 = 16, 16-5 = 11, 11-6 = 5, etc..

Example #2 K is the midpoint of JL. Make a conjecture and draw a figure to illustrate your conjecture. What can you conclude (or make an educated guess) about the pieces of the line JL. Answer: J K L

Counterexample: An example used to show that a given statement is not always true. Example #3: Let’s look at p. 79 in your textbook. Using the graph, find a counterexample to the statement The states with a population increase of less than 1 million people increased their population by more than 25% from 1990 to 2000. Answer: Oregon had an increase in population of less than 1 million, but did not increase its population by more than 25%.

Try these: p. 80 #2, 4, 6 2. 7 4. A, B, C, and D are noncollinear 2. 7 4. A, B, C, and D are noncollinear 6. Michigan has 1,808,000 anglers and North Carolina has 1,641,860 anglers Homework #9: p. 80 7-33 odd, 40-41