Let $ ABCD$ be the convex quadrilateral and $ X,Y,Z,W$ the midpoints of the segments $ AB, BC, CD, DA$, respectively. Consider the lengths $ AB=2x$, $ BC=2y$, $ CD=2z$, $ DA=2w$, $ AC=2s$, $ BD=2t$. By the median theorem for the median $ CX$ in triangle $ ABC$ we have $ 2s^{2}+2y^{2}=x^{2}+(CX)^{2}$ By the same theorem for the medians $ DY,AZ,BW$ in triangles $ BCD,CDA,DAB$, respectively, we obtain equations wich sum (with the previous one too) is $ x^{2}+y^{2}+z^{2}+w^{2}+4s^{2}+4t^{2}=(CX)^{2}+(DY)^{2}+(AZ)^{2}+(BW)^{2}$ In the same way, we can obtain $ x^{2}+y^{2}+z^{2}+w^{2}+4s^{2}+4t^{2}= (DX)^{2}+(AY)^{2}+(BZ)^{2}+(CW)^{2}$