Indirect Proof (Proof by Contradiction)
How to solve indirect proof (proof by contradiction) problems: example and its solution.
How to write?
Indirect proof is a way to prove a statement
when writing two column proof.
Start from assuming that '~prove' is true.
Then show a contradiction.
If there's a contradiction,
the first assumption ('~prove') must be the cause.
So '~prove' is false,
which means 'prove' is true.
Assume that '~prove' is true:
M is the midpoint of AB.
Try to find a contradiction.
Start from the assumption.
AM ≅ MB (by the property of a midpoint)
AM = MB (definition of congruent segments)
AM = MB is derived.
But AM ≠ MB. (given)
Here's a contradiction.
This contradiction is caused by the assumption: '~prove' is true
So '~prove' is false.
And its negation, 'prove' is true.
So 'M is not the midpoint of AB' is true.