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Actually that does apply on a plane only, not on a sphere or otherwise warped plane ;-)
Of course, it applies only in "Euclidean Geometry."
I wonder, has anyone tried to do geometry for UNKNOWN or changing planes? ;-)
I am not sure if i understand your question right, but of course mathematicians have explored the concept of geometry in non-Euclidean spaces, where the traditional rules of Euclidean geometry do not apply. Non-Euclidean geometries, such as hyperbolic and elliptic geometries, deal with planes that have different properties from those of Euclidean space.
I always throw out wildcards whenever I can haha… No mathematician at ALL, but Euclidean geometry has always been a natural for me.
Would need some very weird mathematician to know if any geometry can be done NOT knowing what plane it is on! Or even with a plane that is changing ;-)