Chapter 2 Reasoning and Proof 2 1 Inductive

2. 1 Inductive Reasoning and Conjecture o Conjecture: an educated guess based on o

Example #2 o K is the midpoint of JL. Make a conjecture and draw

Counterexample: An example used to show that a given statement is not always true.

Try these: p. 80 #2, 4, 6 o 2. 7 o 4. A, B,

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Chapter 2 Reasoning and Proof

2. 1 Inductive Reasoning and Conjecture o Conjecture: an educated guess based on o o 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 o K is the midpoint of JL. Make a conjecture and draw a figure to illustrate your conjecture. o What can you conclude (or make an educated guess) about the pieces of the line JL. o Answer: J K L

Counterexample: An example used to show that a given statement is not always true. o 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. o 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 o 2. 7 o 4. A, B, C, and D are noncollinear o 6. Michigan has 1, 808, 000 anglers and North Carolina has 1, 641, 860 anglers o Homework #9: p. 80 7 -33 odd, 40 -41