1. Applying Deductive Reasoning
Geometry 2.3
Applying Deductive Reasoning

2. Deductive reasoning verses Inductive Reasoning
Uses facts definitions, accepted properties, and laws of logic to form a logical argument
Inductive
Specific patterns and examples to form a conjecture

3. Using the Laws of Logic Law of Detachment Law of Syllogism pq pq
p is true
therefore, q is true.
Law of Syllogism
pq
qr,
then pr.
The Law of Syllogism is also known as the Transitive
Property of Conditional Statements.
The law does not say that p (the original condition or fact)
is known to be true. It simply states that if we agree that
the statement pq is true and the statement qr is true,
then we must accept that the statement pr is true.

4. Law of Syllogism and Law of Detachment
If I stay after school, then I will ride the bus. If I ride
the bus, then I will get home after 4 p.m. If I get
home after 4 p.m. then I will not get to watch Scooby-
Doo. If I don’t get to watch Scooby-Doo, then I won’t
get to see “those meddling kids”.
Suppose I stay after school. What can you conclude?
If you know I did not get to see “those meddling kids”.
What can you conclude?
What law does this illustrate?