It is all basically about a single question: are all triangles the same?
In Euclidean geometry the answer is yes, and all other types of geometries (that aren’t based on shaped you can’t even make in the normal euclidean 3D space, like spheres or saddles) the answer is no.
An example for non-euclidean real life geometry is the geometry of the surface of a sphere, where triangles have more than 180°.
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