As Euclidian Geometry is a special case of all geometries, technically they can be the same, but usually are not, depending on the specific non-Euclidean geometry in question.  

For example, as you know, the angles in all triangles in Euclidean geometry must add up to 180º. This is not true in most non-Euclidean geometries; for instance, on the surface of a sphere the angles in a triangle can be between 180º and 540º, while on a hyperbolic paraboloid (a "saddle"), it can be anywhere between 0º degrees and 180º. This is just one property out of many that involve triangles in non-Euclidean geometries.

Since there are many non-Euclidean geometries, is there one in particular you would like to know more about? Or a specific property of triangles you would like an overview of across common geometries?
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