Theorem about collinear points in geometry with the Poincaré half-plane model

Abstract

In a previous paper, we presented the concept of Lobachevskian algebraic distance of the directional segmental-arcs, then looked for the relationship between the Lobachevskian line segments created by intercepting the axes on two fixed Lobachevskian lines.

Applying such results in that paper, we obtained Theorem 2.2 on the collinear conditions of Lobachevskian points in geometry with the Poincaré half-plane model.

Keywords: Lobachevskian algebraic distance, directional segmental-arc, Poincaré half-plane model, Lobachevskian line segment, Lobachevskian line.