In the rough sketch four concurrent lines are drawn in the Poincaré disk model and in the Euclidean model.

[![enter image description here][1]][1]

If angles $ (\alpha,\beta,\gamma,\delta) $  are made at points of concurrency $(o,O)$ between lines $(1,2,3,4)$ in either model, then does the same trig definition of Cross Ratio hold good?

If that is so, and if three adjacent angles are given then they have the ***same Cross Ratio*** in euclidean and hyperbolic geometries. Is this correct ?

  [1]: https://i.sstatic.net/a5eUj.png