Although he presented it differently, the modern version is as follows:
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It is a consequence of Euclids's parallel postulate.
postulate theorems tell that the lines are parallel, but the converse if asking you to find if the lines are parallel.
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.
converse of the corresponding angles postulate