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Derivation of the Pythagorean Theorem

 The Pythagorean Theorem states that squares erected upon the shorter two sides of a right triangle have a total combined surface area equal to the square erected on the hypotenuse or the longest side.

 

 

 

 

Upon adding a few line segments, we see that four identical triangles (1, 2, 3 and 4) are created and are identical in size  to the original triangle.  Examine triangle four and notice which side is A and B.  Notice how the A side of triangle 3 is adjacent to side B of triangle 4.  This means that line segment X is equal to B less A.