Some simple proofs of the Pythagorean theorem

Yesterday we did a fun project on these two questions:

(1) Given a square with area one, find a way to make a square with area 2,

(2) Given a square with area one, find a way to make a square with area 3.

That project is here (where you can see that part 2 gave both kids a lot of trouble):

A neat and easy to state geometry problem

I decided to revisit a piece of that project today to show them that both of their solutions to part 2 were essentially proofs of the Pythagorean theorem.

We started by reviewing yesterday’s project:

Next we talked about how my younger son’s way of constructing the square with area three can be used to prove the Pythagorean theorem:

Finally, we looked at the slightly different way that my older son constructed the square with are 3. This approach proves the Pythagorean theorem in a different way:

This was a fun couple of projects that came from a really innocuous sounding question.