They are not alike euclidean is based on a plane. non-euclidean is based on a sphere, similar to earth. Both forms are correct based on the proof the formulas provide. However neither are 100 percent accurate since, although it looks like earth a sphere it is not. The gravitational pole contributes to earth being misshaped and is more of an oval. True geometry would have to take this in consideration when calculating something as simple as the angles of a triangle.
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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.
The geometry of similarity in the Euclidean plane or Euclidean space.
true
There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.
Euclid developed Euclidean geometry around 300 BC. I cannot get much briefer than that.