As in the following figure of a quadrilateral;If the diagonals are stated to bisect each other, I thought this should hold (considering the bottommost triangle in blue lines); a → + b → 2 + b → − a → 2 = b → But this shows that all quadrilaterals have their diagonals bisecting each other, since this gives b → = b → , which implies it's true for all a → and b → . Which obviously isn't true.Where did my reasoning go wrong?

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As in the following figure of a quadrilateral;If the diagonals are stated to bisect each other, I thought this should hold (considering the bottommost triangle in blue lines);                              a          →                    +                        b          →                      2    +                              b          →                    −                        a          →                      2    =            b      →      But this shows that all quadrilaterals have their diagonals bisecting each other, since this gives             b      →        =            b      →       , which implies it&#039;s true for all             a      →        and             b      →      . Which obviously isn&#039;t true.Where did my reasoning go wrong?

taldenmr · Accepted Answer

The upper right point is not             a      →        +            b      →        in general, if it is then we have a parallelogram, of which the diagonals bisect each other as you have proven.

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