DEDUCTIVE REASONING: Making logical conclusions
based on definitions, theorems (facts) and
Joe was given this square with 4 ≅ sides.What can he conclude?
FACT:IF Quadrilaterals have 4 ≅ sides
THEN the quadrilateral is a rhombus.
It is a quadrilateral.
It is a rhombus.
Inductive reasoning takes specific examples
and makes sweeping general conclusions.
Conclusion by inductive reasoning:
My math teacher is skinny
My last math teacher was skinny
All math teachers are cool
All math teachers are skinny
All math teachers are short.
By inductive reasoning (using the specific
examples to make a general rule to add 10)
the next term is...
Inductive reasoning is used
to find the next term in a pattern:
10, 20, 30, 40, 50,
All even numbers are divisible by 2
28 is even
Therefore 28 is divisible by 2
The next term is going to be 18
My daddy has curly hair
My brother has curly hair
Therefore everyone I am related to has curly hair
An apple a day keeps the doctor away.
Joe ate an apple every day.
Dr. Dre stayed away.
Jimmy got bitten by a dog .
Jimmy is now scared of all dogs.
A line segment is broken in half by it's midpoint.
B is the midpoint of segment AC.
Therefore, BA = BC
(use specific examples to make a general rule)
Two episodes of the Big Bang Theory
made me laugh and laugh LOLOLOLOL
Therefore, The Big Bang Theory is always funny.
Apply a general rule to specific examples)
All right angles = 90 degrees. Two angles with the same measure are congruent.
∡ABC and ∡WXY are right angles.
Therefore, ∡ABC and ∡WXY are congruent.