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.

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.

both the geometry are not related to the modern 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.

There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.