Introduction of measures for segments and angles in a general absolute plane

To an absolute plane (E,L,≡,α)(E,L,≡,α) in the general sense of Karzel et al. [Einführung in die Geometrie, UTB 184, Vandenhoeck, Göttingen, 1973, Section 16] there will be associated an ordered commutative group (W,+,<)(W,+,<) such that (W,+)(W,+) is a subgroup of the corresponding K-loop (E,+)(E,+) of the absolute plane and a cyclic ordered commutative group (E1,·,ζ)(E1,·,ζ) where (E1,·)(E1,·) is isomorphic to a rotation group fixing a point. (W,+,<)(W,+,<), resp. (E1,·,ζ)(E1,·,ζ), will serve to introduce a distance λλ describing the congruence and satisfying the triangular inequality or resp. a measure μμ for angles describing the congruence and conjugacy of angles.