Download PPSection 2.2

Geometry: Section 2.2
Inductive & Deductive Reasoning
What you will learn:
1. Use inductive reasoning
2. Use deductive reasoning
A conjecture is
an unproven statement based on observations.
In science this is called a _____________
hypothesis
Example: Make a conjecture about the
product of an even integer and any other
integer. The product of an even integer and
any other integer is even.
You use inductive reasoning when you find a
pattern in specific cases and then write a
conjecture for the general case.
46,57
25,36
8
2
n 1
32
32
16
To show a conjecture is true, you must show
that it is true for all cases. To show that a
conjecture is false, you simply need to show
one case where the conjecture is false.
A counter example is
a specific case for which the conjecture is false
Example: Show the conjecture is FALSE by finding a
counterexample.
a) All prime numbers are odd.
2 is even and a prime number
b) The sum of 2 numbers is always greater the larger
number.
20 2
or - 3  5  2
Deductive reasoning uses facts, definitions,
accepted properties and the laws of logic to
form a logical argument.
Laws of Logic:
Law of Detachment:
If the hypothesis of a true conditional statement
is true, then the conclusion is also true.
Law of Syllogism:
If hypothesis p, then conclusion q.
If hypothesis q, then conclusion r.
If these statements are true
If hypothesis p, then conclusion r.
This statement is true
Example: Use the Law of Detachment to make
a conclusion from these two statements:
If a figure is a square, then it is a rectangle.
Quadrilateral ABCD is a square
Quad ABCD is a rectangle
If it is rainig today, then you can go to the mall.
No conclusion possible.
Deductive reasoning
Inductive reasoning
HW: pp80 – 82 /
2-8 Even, 14-24 Even, 30-34 Even, 44