# 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.

## Example

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.