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If two parallel lines are cut by a transversal, the corresponding angles are equal.
If a transversal intersects two lines such that a pair of corresponding angles is equal, then the lines are parallel.
If two parallel lines are cut by a transversal, the alternate angles are equal.
If a transversal intersects two lines such that a pair of alternate angles is equal then the lines are parallel.
If two parallel lines are cut by a transversal, the allied angles are supplementary.
If a transversal cuts two lines such that a pair of allied angles are supplementary, then the lines are parallel.
