## Pythagorean Theorem Proof

version = 1.03 of pythagoras.tex 2012 Jun 14

*National Institutes of Health, Frederick National Laboratory for Cancer Research, Gene Regulation and Chromosome Biology Laboratory, P. O. Box B, Frederick, MD 21702-1201. (301) 846-5581, email: schneidt@mail.nih.gov http://alum.mit.edu/www/toms/

Prove the Pythagorean theorem myself with no help. Do it from scratch geometrically.

Equal Areas: triangles d, e, f, g, h, i, j T since they are all 3 × 4.
Any other side sizes also work.

Equal Areas: squares ABCD and EFGH since they are both (3 + 4) × (3 + 4) = 7 × 7

But ABCD = a + b + d + e + f + g = a + b + 4T

and EFGH = c + f + h + i + j = c + 4T

So the areas of the three squares a, b and c are related by:

a + b = c

QED!!!
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