  We describe the point and contact equivalence groupoids of an important class
of two-dimensional quasilinear hyperbolic equations. In particular, we prove
that this class is normalized in the usual sense with respect to point
transformations, and its contact equivalence groupoid is generated by the
first-order prolongation of its point equivalence groupoid, the contact vertex
group of the wave equation and a family of contact admissible transformations
between trivially Darboux-integrable equations.
