  In this paper we deal with $\NIL$ geometry, which is one of the homogeneous
Thurston 3-geometries. We define the "surface of a geodesic triangle" using
generalized Apollonius surfaces. Moreover, we show that the "lines" on the
surface of a geodesic triangle can be defined by the famous Menelaus' condition
and prove that Ceva's theorem for geodesic triangles is true in $\NIL$ space.
In our work we will use the projective model of $\NIL$ geometry described by E.
Moln\'ar in \cite{M97}.
