USAMO 1977 Problem 4

$\mathrm{ABCD}$ is a tetrahedron. The midpoint of $\mathrm{AB}$ is $\mathrm{M}$ and the midpoint of $\mathrm{CD}$ is $\mathrm{N}$. Show that $\mathrm{MN}$ is perpendicular to $\mathrm{AB}$ and $\mathrm{CD}$ iff $\mathrm{AC}=\mathrm{BD}$ and $\mathrm{AD}=\mathrm{BC}$.