Final answer:
The Three-point Geometry uses the hyperbolic parallel postulate.
Step-by-step explanation:
The Three-point Geometry is associated with hyperbolic geometry, which deviates from Euclidean geometry in terms of the parallel postulate. In hyperbolic geometry, given a line and a point not on it, there exist infinitely many lines parallel to the given line through the specified point. This contrasts with Euclidean geometry, where only one such parallel line exists. The hyperbolic parallel postulate is a fundamental distinction that characterizes non-Euclidean geometries, providing alternative frameworks for understanding spatial relationships and challenging traditional geometric assumptions. The Three-point Geometry, rooted in hyperbolic principles, explores these non-Euclidean properties and their implications for geometric structures.