prove a pair of corresponding angles formed by a transversal of two line is congruent then the two lines are parallel
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Euclid's Proposition 27 states that if a transversal intersects two lines so that alternate interior angles are congruent, then the lines are parallel. Second, if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.
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