Query on how to study well in non-Euclidean/ hyperbolic geometry

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I m currently taking a course on non-Euclidean/ hyperbolic geometry, mainly consists of using axioms in these geometries, etc... to proof certain theorems or results.

I am a beginner in these sorts of "non-regular" geometries, and had a hard time of proving things by using only axioms as mentioned above and not theorems from Euclidean geometry, and some of the results in non-Euclidean geometry seems so wield(i.e. Lambert quadrilaterals) as they are different from the Euclidean geometry that I had knew and adapted to from the past.

So now I can only do the proofs very slowly (like finish a few questions in days but not hours) and sometimes can't finish the proof. Plus I don't have much exercise questions to practice on.

Therefore, I did poorly so far in this subject, I want to improve but I can't think of ways for improving.

Are there any suggestions or books/websites/etc... recommendation so that I can understand more clearly in the subject and do proofs faster? Thank you!