Answer
Euclid`s geometry assumes that there is a parallel line to the given line, through a point which is not on the given line.
Work Step by Step
Euclid`s geometry is based on the assumption that if a point which does not lie on the given line, then there must be one line that can be drawn through the point which is parallel to the given line.
Euclid geometry is based on the plane surface.Hyperbolic geometry states that if a point which does not lie on the given line, then there must be an infinite number of lines through that point which do not intersect the given line. Hyperbolic geometry is based on a pseudo sphere surface.
Elliptic Geometry is based on the assumption that there are no parallel lines. This is based on a sphere.
