Yesterday in geometry students were analyzing proofs of the Pythagorean Theorem using this lesson by The Shell Foundation. It ties in nicely with my favorite proof which they discuss while watching this video (there’s something about doing proofs to classical music which delights me).
At the end of class, a student came up to me and asked if there was a theorem which says the following:
I responded that I had no idea if it was a theorem, but if he could prove it, then it would become a theorem and be named after him.
It sure SEEMS like it’s true.
And the above diagram actually satisfies his initial question which was if you have a square, and you draw 4 congruent segments inside the square which intersect the sides of the square, will the resulting figure also be a square?