
Hyperbolic rigid motion
Let $\displaystyle AB$ and $\displaystyle CD$ be geodesic segments of equal length. Prove that there is a hyperbolic rigid motion that maps $\displaystyle A$ and $\displaystyle AB$ onto $\displaystyle C$ and $\displaystyle CD$, respectively.
Once again, completely lost. (Headbang)


Okay, so I know the cases will probably have to divided up depending on if the geodesic segments are vertical lines or arcs of circles centered on the xaxis, and there has to be some inversion(s), but after that point I am just not sure.

so you're using the upper plane model of the hyperbolic geometry, are you?

Yes, the upper half plane, so the hyperbolic rigid motions we have covered so far are inversions where the center is located on the xaxis, horizontal translations, and reflections across vertical lines.