Question 203812
From  "Discovering  Geometry,  an  investigative  approach"  by M  Serra,  Key  Press, 2003,  chpt  9,,pg 463.
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1)  Area  of  large  (a+b)^2,  which  equals a^2 +2ab+b^2
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2) All  small  triangles  are,  A= (1/2) ab
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Total  area  of  4  small  triangles  is, 4* (1/2) ab = 2ab
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Small  "quadrilateral", A= {a^2 +2ab +b^2} -2ab = a^2 + b^2
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3)HOWEVER,  the  small"quadrilateral"  is  a  square,  with  A=c^2
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Therefore, c^2 = a^2 +b^2
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Which  is  the  Pythagorean  Theorem.
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Please  see  page  463,  for  more  detail