Three right-angled triangles have been placed in a halfplane determined by a line $\ell$, each with one leg lying on $\ell$. Assume that there is a line parallel to $\ell$ cutting the triangles in three congruent segments. Show that, if each of the triangles is rotated so that its other leg lies on $\ell$, then there still exists a line parallel to $\ell$ cutting them in three congruent segments.