If there are an infinite number of lines parallel to a given line through a point not on the given line. The geometry that he use as his model is: hyperbolic geometry.
Hyperbolic geometry can be defined as the process in which parallel lines either move toward a direction or move to different or separate direction.
When it comes to hyperbolic geometry there are many parallel lines at a direction that is beyond the line at which two separate lines are parallel to the line that is known or if the line are parallel to a given line through a point not on the given line.
Therefore If there are an infinite number of lines parallel to a given line through a point not on the given line. The geometry that he use as his model is: hyperbolic geometry.
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