Prove that there exists an isometry P in Isom(H^2) such that P(A)=B

Question

Where A and B are ideal triangles in H^2 (upper sheet of hyperboloid). How do I get started with this proof?

Answer 1

This is asssignment question 9.3 here: http://homepages.warwick.ac.uk/~masgar/Teach/2015_MA243/examples9.pdf

Given this, the tags and information given with the question are quite lacking.

HINT

All ideal triangles are congruent to each other.