No, both spherical and hyperbolic geometries are noneuclidian.
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yes
False.
No. Spherical geometry did not disprove Euclidean geometry but demonstrated that more than one geometries were possible. Different circumstances required different geometries. Similarly hyperbolic geometry did not disprove either of the others.
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.