A “new to me” Pythagorean theorm proof from Colin Wright

Saw this post on twitter today and tried to talk through it with my older son this morning:

One nice coincidence was that my son started reviewing geometry today and finished reviewing quadratic equations last week, so Wright’s tweet was a nice way to tie both subjects together.

Unfortunately our 7:00 am talk was derailed when I missed a minus sign and created a mess . . . . So, we revisited the idea when he got home from school.

Also, two notes before diving into the post:

(i) If you’ve seen this proof before, don’t worry, Wright does not claim this proof is original – in fact he claims this this proof is probably well known. As best as I can remember Wright’s post was the first time I’ve seen it.

(ii) I make a slightly different choice of variables than Wright does in his write up.

We started back in this afternoon with a quick review about inscribed circles in a right triangle:

Next we worked through some of the algebraic expressions we found in the last video. He didn’t simplify the expressions in quite the way I was expecting, but what he did was fine.

Finally, we looked at the expression we obtain by squaring the hypotenuse. By a little bit of algebra (which makes for a nice little algebra review for a kid!) we find the hypotenuse squared is equal to the sum of the squares of the other two sides!

Thanks to Colin Wright for posting this nice bit of geometry!

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