Hyperbolic side-side-side congruence
= Hyperbolic side-side-side congruence
Three corresponding side lengths determine a <hyperbolic triangle> up to an <isometry> of the <hyperbolic plane>. First match an ordered pair of vertices by an isometry. The third vertex lies at the intersection of two prescribed hyperbolic distance circles. There are at most two choices, interchanged by reflection in the geodesic through the matched pair; either choice can therefore be matched.