Question

Two lines l and m are perpendicular to line n and p respectively if n and p intersect then prove that l and m also intersect ?

Answer 1

Assume `n` is parallel to `p`. Then two respective perpendiculars `l` and `m` must then themselves be parallel (if they're not the same line). But they're not, they intersect (we have to presume they intersect at just one point), so our assumption is false, so `n` and `p` must intersect as well.