Indirect Proofs
Indirect Proofs
• 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 Proofs
• Indirect Proof:
Assume what you need to prove is false,
and then show that something
contradictory (absurd) happens.
How to Write an Indirect Proof
• Step 1: List givens
• Step 2: Write the negation of what you are trying to prove.
• Step 3: Use logical reasoning to show that the
assumption leads to a contradiction within the proof
• Step 4: Write what you were originally proving for your final
statement, with the reason being contradiction with
the appropriate steps that were contradicted.
(i.e. contradiction 2,5)
How to Write an Indirect Proof
• Examples: State the assumption for starting an
indirect proof
• a. ABC is not equal to XYZ
ABC is equal to XYZ
• b. 3 is an obtuse angle
3 is not an obtuse angle
• c. DEF is an equilateral triangle
DEF is not an equilateral triangle
• d. Points J , K , and L are collinear
Points J , K , and L are not collinear
Pg. 10 #1
Statement
X
Y
1. XZ  YZ
2. X  Y
1. Given
3. XZ  YZ
3. Sides opposite
congruent angles in a
triangle are congruent
4. Contradiction 1,3
Z
4. X  Y
Given : XZ  YZ
Prove : X  Y
Reason
2. Assumption