Hyperbolic Geometry

Explore to see if the following theorems of plane geometry still hold true under hyperbolic geometry.
The medians of a triangle are concurrent.
The heights of a triangle are concurrent.
The perpendicular bisectors are concurrent.
The angle bisectors of a triangle are concurrent.
External angle bisectors are concurrent.

Construct the counterpart of these theorems under the hyperbolic geometry:

Pappus Theorem.
Pascal Theorem
Desargues Theorem