Referring to the axiomatic bases of two-dimensional geometries according to Cayley-Klein and their projective interpretations, we have examined parallelism of an isotropic and ideal line in geometries which have the same projective metrices on a line or a pencil of straight lines. In terms of these examinations for autodual HH-geometry (a geometry in which the projective metrices on a line and a pencil of lines is hyperbolical, and whose axiomatics is not known to us) we have concluded the following: a) in the HH-geometry the Lobatchewskian axiom is true; and b) besides the line as the starting notion, the HH-geometry contains both isotropic and ideal lines which are to be either considered starting notions during the axiomatic development of this geometry or defined.