  We define transversal tropical triangles (affine and projective) and
characterize them via six inequalities to be satisfied by the coordinates of
the vertices. We prove that the vertices of a transversal tropical triangle are
tropically independent and they tropically span a classical hexagon whose sides
have slopes $\infty,0,1$. Using this classical hexagon, we determine a
parameter space for transversal tropical triangles. The coordinates of the
vertices of a transversal tropical triangle determine a tropically regular
matrix. Triangulations of the tropical plane are obtained.
