Proof by contradiction is a logical mind skill used to reduce a premise or assumption to the absurd, or impossible contradiction. This logical mind game is mastered in logic, but brushed up against in geometry. We play a tug of war game with logic in Geometry. We acknowledge the existence of logic just enough to use some of its powers for our benefit, while also keeping our distance. After all, we don't want to have to get into contrapositives and the square of opposition.
Here's how the proof by contradiction works in mathematics:
Prove that 24 is an even number.
Assume that 24 is not even
if 24 is not even then there is no number that splits 24 in half
there is a number that splits 24 in half (notably:12. This contradicts the previous line)
therefore, 24 is even
In everyday life, the proof by contradiction looks like this:
Prove that your son forgot to put gas in the car
Assume that he did put gas in the car (we always want to assume the best of our kids)
If he put gas in the car then you can drive to work without running out of gas (driving to work is good)
run out of gas driving to work (being stuck on the side of the road is bad - also contradicts the good from the previous line)
therefore, he didn't put gas in the car (bummer)
Do you see how useful this technique that we learn in Geometry can be?