Transcript 2.4-2.5 Deductive Reasoning and Postulates PPT

2.4 Deductive Reasoning
2.5 Postulates
Geometry R/H
Students will be able to distinguish between
Inductive and Deductive Reasoning, and to
determine the validity of a conjecture.
Deductive Reasoning
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To review, when you make a conclusion based on
a pattern of observations, you are applying
inductive reasoning.
We also know how to show that a conditional is
false – find a counterexample. But how do we
show that a conditional is true?
We must use deductive reasoning.
Deductive reasoning is the process of using logic
to draw conclusions from given facts, definitions
and properties.
Example 1: Media Application
Is the conclusion a result of inductive or
deductive reasoning?
There is a myth that you can balance an egg
on its end only on the spring equinox.
A person was able to balance an egg on July
8, September 21, and December 19.
Therefore this myth is false.
Since the conclusion is based on a pattern of
observations, it is a result of inductive
reasoning.
Check It Out! 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, so it
is a result of deductive reasoning.
Applying Deductive Reasoning
See if you can draw a correct conclusion
from the following information.
Given: If a team wins 10 games, then they
play in the finals. If a team plays in the
finals, then they travel to Boston. The
Ravens won 10 games.
Conclusion: The ravens will travel to Boston.
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Inductive or Deductive Reasoning
1. By observing many individual cases, people
concluded that malaria was caused by
breathing air in swampy areas.
2. All students must study Algebra I before
studying Geometry. Mia is studying
Geometry. Therefore, Mia has studied
Algebra I
3. Any quadrilateral with four congruent
angles is a rectangle. A square has four
congruent angles. A square is a
rectangle.
4. I see that every time it rains Sally has
an umbrella. I saw Sally with an umbrella
on Tuesday. Therefore it must rain on
Tuesday.
Summary:
Is the conclusion a result of inductive or
deductive reasoning?
1. At Colonia High School, students must
pass Geometry before they can take
Algebra 2. Emily is in Algebra 2, so
she must have passed Geometry.
Valid Conclusions
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When a conclusion is based on logical
reasoning and facts then we say the
conclusion is valid.
If the reasoning is not logical, then the
conclusion is not valid.
Look at the following conclusions to see
if they are valid or not.
Summary:
Determine if each conjecture is valid?
2. Given: If a person is able to vote in a U.S.
election, they must be at least 18 years old.
Joe is 18 years old.
Conjecture: Joe voted in the last election.
3.
Given: Two angles that are congruent have the
same measure. The measures of two vertical
angles are the same.
Conjecture: The two vertical angles must be
congruent.
Look to Word Document
MORE DEDUCTIVE
REASONING EXAMPLES
FHS
Unit B
11
2.5 Vocabulary
• postulate
• axiom
• proof
• theorem
Concept
Concept
Example 1
Analyze Statements Using Postulates
A. Determine whether the following statement is always,
sometimes, or never true. Explain.
If plane T contains
plane T contains point G.
contains point G, then
Example 2
Analyze Statements Using Postulates
B. Determine whether the following statement is always,
sometimes, or never true. Explain.
contains three noncollinear points.
Example 3
A. Determine whether the statement is always, sometimes,
or never true.
Plane A and plane B intersect in exactly one point.
A. always
B. sometimes
C. never
Example 2
B. Determine whether the statement is always, sometimes,
or never true.
Point N lies in plane X and point R lies in plane Z.
You can draw only one line that contains both points N and
R.
A. always
B. sometimes
C. never
Concept
Concept
Homework
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Deductive versus Inductive Reasoning
Worksheet
Book Work for Section 2.5
Pg. 130 #1-9 odd, 10-13 all, 17-29 odd,
34-40 even