Hyperbolic geometry question concerning lengths between parallel lines

Question

Theorem (H16). If:

1. $l$ and $m$ are parallel lines,

2. $j$ is a common perpendicular intersecting $l$ at point A and $m$ at point B, and

3. C and E are points on $l$ so that C is between A and E,

Then:

1. $L$(C; m) > $L$(AB);

and

2. $L$(E; m) > $L$(C; m).

I wish I knew how to even begin this proof, but I'm really not sure how to. Can anyone please offer me some help or advice on how I can approach this proof?

Answer 1

Just as similar questions with Euclidean geometry are done with ordinary trigonometry, this is easy to do with hyperbolic trigonometry. Here's a web link, but I would recommend getting a textbook such as Ratcliffe's book.