Each of the four right triangles are of equal size with area equal to

½AB

The A-side angle and B-side angle of each of these triangles are complementary angles, so each of the angles of the blue area in the middle is a right angle, making this area a square with side length C. The area of this square is C^{2}. Thus the area of everything together is given by:

However, as the large square has sides of length A + B, we can calculate its area as (A + B)^{2}. We can expand this to A^{2} + 2AB + B^{2}. So

4(½AB) + C^{2} = A^{2} + 2AB + B^{2}

2AB + C^{2} = A^{2} + 2AB + B^{2}

C^{2} = A^{2} + B^{2}

Q.E.D.

So that's the plan for now. I teach the lesson this coming Friday. I'll let you know how it goes. Right now, I'm off to take the Praxis I. Wish me luck.

^{}

## 1 comment:

i love this one.

i'm pretty consistent about

including the other diagram

(next to "similarity proof"

and labelled "proof by area

subtraction" in the (what else?)

wikipedia page on the p'an thm:

as clear an example as i know

of a "proof from the book".

Post a Comment