First we note that there are two different cases: Either the line connecting $X$, $Y$ and $Z$ intersects two sides of the triangle or none of them. So in the first case that it intersects two of the triangle’s sides we get the following picture:

From this we follow ($h_{1}$, $h_{2}$ and $h_{3}$ being undircted):

Mulitplying all this we get:

The second case is that the line connecting $X$, $Y$ and $Z$ does not intersect any of the triangle’s sides:

In this case we get:

So multiplication again yields Menelaus’ theorem.