### Pythagorean theorem

 To prove the Pythagorean theorem, construct two identical squares from the sum of two arbitrary lengths, a and b: The four shaded right triangles in the left square are congruent with the four shaded right triangles in the right square.  The shaded areas can, therefore, be removed from both squares while preserving equality.  (When equals are subtracted from equals, the remainders are equal.) QED: $\LARGE c^{2}=a^{2}+b^{2}$ Copyright © 540 BC, Pythagoras of Samos