Question: Playfair's Postulate: for every line l and every point P not on l, there is a unique line m parallel to l containing P. The

Playfair's Postulate: for every line l and every point P not on l, there is a unique line m parallel to l containing P.

The Euclidean Parallel Postulate: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.

Prove that in neutral geometry, the Euclidean parallel postulate implies Playfair's postulate.That is, assume Euclid's Parallel Postulateand prove Playfair's Postulate.

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