Honors Geometry
Intro. to Deductive Reasoning
Reasoning based on observing
patterns, as we did in the first
section of Unit I, is called inductive
reasoning. A serious drawback with
this type of reasoning is
your conclusion is not always true.
The logic chains we worked with in Section
2.2 are examples of deductive reasoning.
*Deductive reasoning is reasoning
based on logically correct conclusions
Deductive reasoning
always give a correct conclusion.
We will reason deductively by doing two
column proofs. In the left hand column,
we will have statements which lead from
the given information to the conclusion
which we are proving. In the right hand
column, we give a reason why each
statement is true. Since we list the given
information first, our first reason will
given Any other reason must
always be ______.
theorem
be a _________,
definition _________
postulate or ________.
A theorem is a statement which
can be proven.
We will prove our first theorems
shortly.
Our first proofs will be algebraic
proofs. Thus, we need to review
some algebraic properties. These
properties, like postulates are
accepted as true without proof.
Reflexive Property of Equality:
a=a
Symmetric Property of Equality:
If a = b, then b = a
Addition Property of Equality:
If a = b, then a+c = b+c
Subtraction Property of Equality:
If a = b, then a-c = b-c
Multiplication Property of Equality:
If a = b, then ac = bc
Division Property of Equality:
If a  b and c  0, then a  b
c
c
Why must we say c  0?
Because division by 0 is undefined!
Substitution Property:
If two quantities are equal, then
one may be substituted for the
other in any equation or
inequality.
Distributive Property
(of Multiplication over Addition):
a(b+c) = ab + ac
Example: Complete this proof:
Given
Multiplication Property
Distributive Property
Addition Property
Division Property
Example: Prove the statement:
1. 2x - 6  5x  4 1. Given
 10
) x
3