Why Does a² + b² = c²?

Visual proof of the Pythagorean Theorem

As an 8th grade math teacher, teaching the Pythagorean Theorem was one of my favorite topics. For some reason, kids love it, even the ones who typically struggle and dislike mathematics.

Why we love the Pythagorean Theorem

I think the Pythagorean Theoreom tends to be loved by students is because

• It has a fun name,
• And an easy-to-remember formula,
• Where the math itself is relatively easy,
• And everyone in the class starts off on the same level, as usually there is not much previous work the math builds off of compared to other lesson topics

Students zip through problems, plugging squares and square roots in their calculators and feeling successful at their new mastery.

But why does the Pythagorean work?

It seems so magical and strange that this fun and simple formula works perfectly for every right triangle in our Euclidean world. Is it just by chance?

I think the proofs of the theorem are just as fun as solving the formula itself, so let’s go through a famous one.