both the geometry are not related to the modern geometry
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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
In Euclidean geometry parallel lines are always the same distance apart. In non-Euclidean geometry parallel lines are not what we think of a parallel. They curve away from or toward each other. Said another way, in Euclidean geometry parallel lines can never cross. In non-Euclidean geometry they can.
Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few
The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.
Geometry that is not on a plane, like spherical geometry