Abstract To an absolute plane ( 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 , + , < ) such that ( W , + ) is a subgroup of the corresponding K-loop ( E , + ) of the absolute plane and a cyclic ordered commutative group ( E 1 , · , ζ ) where ( E 1 , · ) is isomorphic to a rotation group fixing a point. ( W , + , < ) , resp. ( E 1 , · , ζ ) , will serve to introduce a distance λ describing the congruence and satisfying the triangular inequality or resp. a measure μ for angles describing the congruence and conjugacy of angles.