if a transversal intersects two lines such that, either.
(a). any one pair of corresponding angles is equal,or
(b). any one pair of alternate interior angles is equal, or
(c). any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.
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Conversely, if a transversal intersects two lines such that a pair of interior angles are equal, then the two lines are parallel. As per the co-interior angles theorem, if a transversal intersects two parallel lines, each pair of co-interior angles is supplementary (their sum is 180°).
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