Reasoning - The logic of Geometry that involves the derivation of conclusion supported by a statement
Kinds of Reasoning
1. Intuition
> guessing
> no formal process
> no need for mathematical proof
2. Analogy
> comparison
> if one aspect they are alike then in all aspects they are alike
3. Induction
> specific to general
> allows to reach conclusion based on a pattern of specific events
4. Deduction
> general to specific
>also the process of drawing a conclusion based from something known/assumed
examples:
intuition
- because of the dark clouds; conclusion: it's going to rain
-after the first meeting of geometry class, Cassy says to herself "I think I'm going to like Geometry"
analogy
- hair : humans; feathers : birds
- deliver : mail man ; receive : recipient
induction
- 1 * 9 = 9, 2 * 9 = 18, 3 * 9 = 27,..10 * 9 = 90
The products, of factors (1 - 10) multiplied to 9, all come up with a sum of 9 if the units and tens place are added. So the 45 which is the product of 5 & 9, when the units and tens are added give a sum of nine. (5 + 4 = 9)
-1 squared, 3 squared, 5 squared, 7 squared...
When an odd number is squared by itself, its product is odd as well. So 11 squared which is an odd number must give an odd number as well ( 11 * 11 = 121)
deduction
-Insects have 6 legs. A bee which has six legs must be an insect.
- During the Dark Age, learning was banned. So painting which is a form of learning was also banned during the Dark Age.
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