Sum of interior angles of triangle

Dragging the vertices out towards the boundary we can approach the trebly asymptotic triangle, and if we drag the vertices very close to each other we see that the triangle looks much like the Euclidean case.

That the sum is less than Pi is equivalent to the two parallel postulate for this geometry and this fact together with the sum of the angles of a quadrilateral has to be less than 2Pi, is often used in proofs concerning figures and theorems that are different to those of Euclidean geometry.