Here is a Hyperbolic Geometry proof that I am asked to solve:
Prove that if a transversal crossing two parallel lines contains the midpoint of a common perpendicular to those lines, then the alternate interior angles are congruent.
Here is my diagram: https://drive.google.com/open?id=1-PSyMXqtOoOYtZT6x985K7pDZ05aLcrw
Basically, my idea was to create two triangles and show that they are congruent. The midpoint of the perpendicular creates two congruent sides, the vertical angles are congruent, and the right angles are congruent. So the two triangles are congruent by ASA and therefore, the alternate interior angles are congruent by CPCTC. My concern is that some of my methods are not allowed in hyperbolic geometry and I am unsure if this is an issue here.