Soit $(\vv{x},\vv{y})\in E^{2}$. On a :
$$\begin{array}{rcl}\vv{x}\perp\vv{y} & \iff & \varphi(\vv{x},\vv{y})=0 \\ & \iff & \|\vv{x}\|^{2}+\|\vv{y}\|^{2}+2\varphi(\vv{x},\vv{y})=\|\vv{x}\|^{2}+\|\vv{y}\|^{2} \\ & \iff & \|\vv{x}+\vv{y}\|^{2}=\|\vv{x}\|^{2}+\|\vv{y}\|^{2} \end{array}$$