Hyperbolic triangle

As in the Euclidean case, a hyperbolic triangle, is determinated by three points not lying in the same line.

To form a triangle we have to join this three points, in pairs, by segments. As the tool that allows us to construct segments is only defined when the endpoints do not belong to the same Euclidean line perpendicular to the boundary line, we will suppose that the three points that describe us the triangle are not in this situation.

We could think that if two points are in the last situation they can be joined by an Euclidean segment since this Euclidean segment and the hyperbolic segment coincide, but we can not make this if we want the constructions to be interactive since in this case the Euclidean segment will continue being Euclidean and it will not be converted into an arc of circumference.

So, to construct a hyperbolic triangle, it is only necessary to open a new Sketch, draw the boundary line from two points A and B and fix three points in the allowed position. Now, with the hyperbolic segment tool we draw the three sides of the triangle.

List of tools

Triangles

Hyperbolic geometry