Demonstration:Sum of the angles of the hyperbolic triangle
In figure is shown a hyperbolic triangle with sides DG, DF and GF that are arches with centre C, E and H respectively. The tangents are not shown for reasons of clarity of the figure but, someone wants them let their display be done. In figure are shown the exterior angles (denoted by α,β and γ) of the angles between two tangents passing through the vertices. The sum of the interior angles of the hyperbolic triangle can be computed using the expression: δ=540°-(α+ β+ γ).
To bring the triangle to sight use the GeoGebra tools.