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Parallel lines and Transversal

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Theorem : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

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Theorem : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.

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Theorem : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

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Theorem : If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.

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exterior angles, interior angles, consecutive interior or allied angles or co-interior angles