  In this paper we study the joint distributions of the telegraph process and
its maximum conditioned on the number of changes of direction and the initial
velocity. We prove that in the case of positive starting velocity, a form of
the reflection principle holds. We call it the negative reflection principle
and we generalize it to the paths of the random motions moving with constant
finite velocity. In the last section we obtain the conditional distribution of
the first passage time of the telegraph process by using the known results on
the maximum of the motion. Finally, we derive the distribution of the first
returning time to the origin.
