In school, I recently proved a solid geometry excercise by assuming that the following lemma is true:
If two lines $g$ and $h$ in the euclidian space are not parallel, and if the lines seem parallel under a parallel projection, then the distance between projected lines is equal to the minimal distance of the $g$ and $h$.
Is this true, and if yes, how can I prove it? Please try to prove it in a way, that is understandable for somebody in highschool. (An answer of the style "This is just a special case of lemma X" is not very helpful)