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| Allied Angles Axiom |
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| (Adjacent interior angles on the same side of a transversal are called allied angles). |
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| If two parallel lines are cut by a transversal, then the allied angles are supplementary. |
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 and  |
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| A transversal cuts two lines. If the allied angles are supplementary, then the lines are parallel. |
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If  or  , in the following figure then AB is parallel to CD. |
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