We will now prove the Pythogorian theorem:

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

i.e, If a and b are the legs and c is the hypotenuse then  a 2 + b 2 = c 2 .

Proof:  We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: ( a + b ) 2 = c 2 + 4 ( 1 2 a b )                                a 2 + 2 a b + b 2 = c 2 + 2 a ba 2 + b 2 = c 2

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