An h-altitude of a hyperbolic triangle is an h-segment
through a vertex perpendicular to the opposite side.
The Altitudes Theorem for Hyperbolic Triangles
Let ABC be an h-triangle, and let the h-altitudes be
AQ, BR and CP.
Since the labelling of the vertices is immaterial, we may as
If <ABC is a right angle, then AB and CB are h-altitudes,
In the CabriJava figure on the right, we can move B to see
This is an easy consequence of the very important
Thus, we see that, either all the h-ratios are positive, or just
Consider the case where the angles are acute.
If the angle at B is obtuse, then we need to replace
Thus, by the Converse of Ceva's Theorem,
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