Menelaus’ theorem

If the points $X$, $Y$ and $Z$ are on the sides of a triangle $ABC$ (including their prolongations), collinear and do not coincide with any of the points $A$, $B$ and $C$, then the equation

$$\frac{AZ}{ZB}\cdot \frac{BY}{YC}\cdot \frac{CX}{XA}=-1$$

holds (all segments are directed line segments). The converse of this theorem also holds (thus: three points on the prolongations of the triangle’s sides are collinear if the above equation holds).