Lesson 2-3: Deductive Reasoning
TARGETS
• Use the Law of Detachment.
• Use the Law of Syllogism.
LESSON 2-4: Deductive Reasoning
Have you ever tried to convince
someone of something using
facts and arguments?
Deductive Reasoning!!!!!!
LESSON 2-4: Deductive Reasoning
Deductive Reasoning
Uses facts, rules, definitions, or properties to reach
logical conclusions
**It is very important not to assume anything more than**
exactly what is written
LESSON 2-4: Deductive Reasoning
EXAMPLE 1 Inductive and Deductive Reasoning
Determine whether the conclusion is based on inductive or
deductive reasoning.
A. In Miguel’s town, the month of April has had the
most rain for the past 5 years. He thinks that April will
have the most rain this year.
B. Sandra learned that if it is cloudy at night it will not be as
cold in the morning than if there are no clouds at night.
Sandra knows it will be cloudy tonight, so she believes it
will not be cold tomorrow morning.
LESSON 2-4: Deductive Reasoning
EXAMPLE 1 Inductive and Deductive Reasoning
Determine whether the conclusion is based on inductive or
deductive reasoning.
C. Every time Kennedy has skipped studying for a
science test, she has gotten at least six wrong.
Kennedy skipped studying for her science test today,
so she concludes that she will get at least six wrong.
D. If Cale is late enrolloing for summer school, he will be
assessed a late fee of $30. Cale has enrolled late this
summer, so he concludes that he will be assessed a late fee
of $30.
LESSON 2-4: Deductive Reasoning
EXAMPLE 2 Use the Law of Detachment
Determine whether the conclusion is valid based on the
given information. If not, write invalid. Explain your
reasoning.
A.
Given: • If a point is a midpoint of a segment, then it divides
the segment into 2 congruent segments.
• W is the midpoint of DC.
DW  WC
Conclusion:

LESSON 2-4: Deductive Reasoning
EXAMPLE 2 Use the Law of Detachment
Determine whether the conclusion is valid based on the
given information. If not, write invalid. Explain your
reasoning.
B.
Given: • If Billy goes to the gym, he will wear athletic socks..
• Billy is wearing athletic socks.
Conclusion: Billy is at the gym.
LESSON 2-4: Deductive Reasoning
EXAMPLE 3 Judge Conclusions Using Venn Diagrams
Determine whether the conclusion is valid based on the
given information. If not, write invalid. Explain your
reasoning using a Venn diagram.
A.
Given: • If a boy is in choir, then he is not in band.
• Kyle is a boy who is not in band.
Conclusion: Kyle is in choir.
LESSON 2-4: Deductive Reasoning
EXAMPLE 3 Judge Conclusions Using Venn Diagrams
Determine whether the conclusion is valid based on the
given information. If not, write invalid. Explain your
reasoning using a Venn diagram.
B.
Given: • If a triangle is equilateral, then it is an acute
triangle.
• The triangle is equilateral.
Conclusion: The triangle is acute.
LESSON 2-4: Deductive Reasoning
EXAMPLE 4 Use the Law of Syllogism
Use the Law of Syllogism to determine whether a valid
conclusion can be reached from each set of statements.
A.
(1) If a figure is a square, then it has four right right angles.
(2) Figure with four right angles is a rectangle.
LESSON 2-4: Deductive Reasoning
EXAMPLE 4 Use the Law of Syllogism
Use the Law of Syllogism to determine whether a valid
conclusion can be reached from each set of statements.
B.
(1) Perpendicular lines form right angles.
(2) The sum of complementary angles equals 90.
LESSON 2-4: Deductive Reasoning
EXAMPLE 5
Apply Laws of Deductive Reasoning
Draw a valid conclusion from the given statements, if
possible. Then state whether your conclusion was
drawn using the Law of Detachment or the Law of
Syllogism. If no valid conclusion can be drawn, write no
conclusion and explain your reasoning.
Given: If it snows more than 5 inches, school will be
closed. It snows 7 inches.
LESSON 2-4: Deductive Reasoning
EXAMPLE 5
Apply Laws of Deductive Reasoning
Draw a valid conclusion from the given statements, if possible.
Then state whether your conclusion was drawn using the Law of
Detachment or the Law of Syllogism. If no valid conclusion can
be drawn, write no valid conclusion and explain your reasoning.
Given: (1) If 2 angles form of a linear pair, then they are
supplementary.
(2) If 2 angles are supplementary, then the sum of the
angles equals 180.