The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then considered parallel if their chords fail to intersect and are perpendicular under the following conditions, 1. If at least one of l and m is a diameter of the disk, they are hyperbolically perpendicular iff they are perpendicular in the Euclidean sense. 2. If neither is a diameter, l is perpendicular to m iff the Euclidean line extending l passes through the pole of m (defined as the point of intersection of the tangents to the disk at the "endpoints" of m).

hyperbolic geometry | Poincaré hyperbolic disk