The following is sort of a converse to the Parallel Projection
Theorem. Let l (ell, not one), m, and n be distinct lines, with m || n. Let lines t and t' be transversals that intersect l, m, and n in A, B, C,
and A', B', C', respectively. Show that if AB/BC = A'B'/B'C',
then line l is parallel to lines m and n. (Note that there are two cases:
line l may or may not be "between" lines m and n, where
"between" is entirely informal here!)