﻿ Indirect Proof. How to write indirect proofs that employ proof by contradiction: for triangles, segments, perpendicular lines

# Indirect Proof

Indirect proof is synonymous with proof by contradiction. A keyword signalling that you should consider indirect proof is the word 'not'. Usually, when you are asked to prove that a given statement is NOT true, you can use indirect proof by assuming the statement is true and arriving at a contridiction.The idea behind the indirect method is that if what you assumed creates a contradiction, the opposite of your initial assumption is the truth.

### Example of an Indirect Proof

Prove that $$\angle$$BDA is not a straight angle.

Statement Reason
1) $$\angle$$BDA is a straight angle 1) (Assumpe opposite \)
2) m$$\angle$$BDA = 180° 2) Definition of a striaght angle
3)AD $$\perp$$ BC 3) Given
4) $$\angle$$BDA is a right angle 4) definition of perpendicular lines
5) m $$\angle$$BDA = 90° 5) definition of a right angle
6) m $$\angle$$BDA is not a straight angle contradiction of steps 2 and 5
7 $$\angle$$BDA is not a straight angle due to the contradiction between 2 and 5, we know that the assumption that WE INTRODUCED in the first step ($$\angle$$bda is a straight angle) is false. Therefore, the opposite must be true: $$\angle$$ is not a straight angle

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