Question 3
Let $ABCD$ be a tetrahedron, and let $A',B'$ be the orthogonal projections of $A,B$ onto their opposite face planes. Prove that the lines $AA'$ and $BB'$ intersect if and only if $AB$ and $CD$ are perpendicular. If $AC=AD=BC=BD$, do $AA'$ and $BB'$ intersect?