Question

If the interior angles formed by a transversal of two distinct lines are complementary,then the two lines are parallel.

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Answer 1

Answer:

It follows from Euclid's parallel postulate that if the two lines are parallel, then the angles of a pair of consecutive interior angles of a transversal are supplementary (Proposition 1.29 of Euclid's Elements). If one pair of consecutive interior angles is supplementary, the other pair is also supplementary.