Pythagorean Theorem - Incomplete proofThe image below is supposed to prove Pythagorean Theorem (without words). However, I see that it is assuming that the square of side c can be inscribed in the square of side a+b and would result in the 4 triangles of equal area. This fact is only assumed, so would the proof be considered incomplete?

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Christina Ward · Accepted Answer

Theorem :In a right triangle with legs a,b and hypothenuse c:      a    2    +      b    2    =      c    2    ..Geometric proof:Consider a square of side length a+b (drawing).Partition the sides into a and b as shown.Each of the 4 corner triangles formed are congruent by SAS, i.e. a,b, and right angle between.Hence the quadrilateral formed by connecting the partition points has 4 equal sides c, a rhombus.The adjacent sides of the inner quadrilateral are perpendicular (why?).Hence the inner quadrilateral is a square.Area of outer square of side length a+b:  A  :=  (  a  +  b      )    2    ..Also:  A  =  4  (  1      /    2  )  a  b  +      c    2  , where (1/2)ab is the area of one triangle (why?).Finally:      a    2    +      b    2    =      c    2  .

Pythagorean Theorem - Incomplete proof The image below is supposed to prove Pythagorean Theorem (wi

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