Geometry Notes1.1 Patterns and Inductive Reasoning

Mr. Belanger

Inductive ReasoningInductive Reasoning

Reasoning based on patterns you observe.

I am COOL, I am COOL, I am COOL,

What do you observe???

ExamplesExamples

3, 6, 12, 24, ….. What do you notice?

Next number is previous times 2.

80, 40, 20, 10, ….. Previous number divided by 2.

Next shape?? Triangle.

ConjectureConjecture

Conclusion you reach using inductive reasoning. (Not thinking and figuring it out, but the actual written answer)

1, 4, 16, 64, ….

Multiplying previous number by 4.

conjecture

CounterexampleCounterexampleExample that proves a conjecture false (untrue)

The sky is blue!

conjecture

Counterexample – raining outside (sky is gray)

You only need to provide ONE counterexample to disprove a conjecture.

ExamplesExamples1) The square of any number is greater than the original.

648

10010

42

2

2

2

0625.25.

11

00

2

2

2

counters

ExamplesExamples

2) The product of two positive numbers is greater than both numbers.

60106

48124

632

5.135.

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