Na Kleinovom modelu hiperboličke ravnine definirana je centralna involutorna kolineacija, koja preslikava granične točke H-ravnine u granične, prave točke u prave, a idealne u idealne. Zovemo ju osna simetrija ukoliko je centar idealna točka, a centralna simetrija ako je centar prava točka, jer imaju sva svojstva istoimenih kolineacija euklidske ravnine. Pomoću osne i centralne simetrije konstruirane su osno-simetrične i centralno-simetrične slike pravaca, točaka i trokuta, simetrale kutova i dužina. Na kraju je riješen jedan složeniji metrički zadatak.On the Klein\u27s model of the hyperbolic plane the harmonic homology is defined. This collineation maps absolute points of the h-plane onto absolute points, real points onto real points and ideal points onto ideal points. It is called line symmetry if the center of collineation is ideal point and point symmetry if the center is real point, because described mappings have equal properties as the analogues mappings in the Euclidean plane. By using point and line symmetries, symmetric images of the lines, points and triangles, bisectors of the angles and perpendicular bisectors of the segments are constructed. At the end one complicated metric problem is solved
