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Euclidian geometry states the 'parallel postulate', in which "if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles."
This postulate is not trivial, and it as been proven that such a proof is impossible. A branch of geometry called non-Euclidian geometry defies this postulate.