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The postulate that pertains to a line is:For any two points there exists only one line.
converse of the corresponding angles postulate
euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.
This is Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.
ONLY a line can be formed by the intersection of two planes...and always.