
When trying to prove a statement is true, it may
be beneficial to ask yourself, "What if this statement was not
true?" and examine what happens. This is the premise of
the Indirect Proof or Proof by Contradiction.
Indirect Proof:
Assume what you need to prove is false, and
then show that something contradictory (absurd) happens.


Steps in an Indirect Proof:
 Assume that the opposite of what you are
trying to prove is true.
 From this assumption, see what conclusions can be
drawn.
These conclusions must be based upon the assumption and the use of valid
statements.
 Search for a conclusion that you know is false
because it contradicts given or known information.
Oftentimes you will be contradicting a piece of GIVEN information.
 Since your assumption leads to a false conclusion,
the assumption must be false.
 If the assumption (which is the opposite of what you are
trying to prove) is false, then you will know that what you are trying to prove must be
true.

How to Recognize When
an Indirect Proof is Needed: 
Generally, the word "not" or the presence of a "not
symbol" (such as the not equal
sign
) in a problem indicates a need for an Indirect Proof.


Proof by Contradiction
is also known as
reductio ad absurdum
(which from Latin means
reduced to
an absurdity). 

Example:
(done in a twocolumn format)
In the accompanying diagram,
is not isosceles.
Prove that if altitude
is drawn, it will not bisect
.

In this example, we must first clearly
indicate the GIVEN and the PROVE. 
Given:


Prove: 


