Using Deductive Reasoning
2-3 to Verify Conjectures
Objective
Understand the difference between
inductive and deductive reasoning.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Vocabulary
deductive reasoning
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
REMEMBER…..
Inductive reasoning is the process of
reasoning that a rule or statement is true
because specific cases are true. You may use
inductive reasoning to draw a conclusion from
a pattern.
How does It apply to Geometry?
Used to form a hypothesis which we can test
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Deductive reasoning is the process of using
logic to draw conclusions from given facts,
definitions, and properties.
How does It apply to Geometry?
Deductive reasoning is the way conclusions are
drawn in geometric proofs.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Inductive
Reasoning
Uses specific examples to
make a general “rule”
Finding patterns or
stereotypes
My Last year’s Math teacher
is awesome.
My Math teacher of this year
is awesome.
Therefore, all GR Math
teachers are awesome.
10, 20, 30, 40, 50…
Using the pattern, the rule
would be add 10 and the next
number would be 50
Holt McDougal Geometry
VS
Deductive
Reasoning
Takes a general rule and uses
it to make a more specific
example
Drawing conclusions from
previous known facts &
definitions
Quadrilaterals have four sides
therefore, a square is a
quadrilateral.
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 1
Is the conclusion a result of inductive or
deductive reasoning?
There is a myth that the Great Wall of China is the
only man-made object visible from the Moon.
The Great Wall is barely visible in photographs
taken from 180 miles above Earth. The Moon is
about 237,000 miles from Earth. Therefore, the
myth cannot be true.
The conclusion is based on logical reasoning from
scientific research. It is a result of deductive
reasoning.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Example 2
There is a myth that an eelskin wallet will
demagnetize credit cards because the skin of the
electric eels used to make the wallet holds an electric
charge.
However, eelskin products are not made from
electric eels. Therefore, the myth cannot be
true. Is this conclusion a result of inductive or
deductive reasoning?
The conclusion is based on logical reasoning from
scientific research. It is a result of deductive
reasoning.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Check it out
Inductive Vs. Deductive
•I saw all students parked illegally got tickets, Joe
parked illegally. Therefore, Joe will get a ticket.
•When I study hard, I will get a good grade. When
I get a good grade, My parents are happy.
When I study hard, my parents are happy.
•Ms Zhang gave out chocolate yesterday. She
gave out chocolate today. I think she will give out
chocolate tomorrow too.
Holt McDougal Geometry
Using Deductive Reasoning
2-3 to Verify Conjectures
Check it out
Inductive vs. Deductive
•The Ridger's Basketball Team scored over 75
points in each of the ten straight games. The
newspaper predicts they will score more than 75
points tonight.
•3,6,9,12,15…The next item based on the pattern
will be 18.
•Two angles are supplementary, One of the angles
is 80 degrees so the other angle must be 100
degree.
Holt McDougal Geometry