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How do you prove that if two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, the lines are parallel?

Answer :

Final answer:

When two lines are cut by a transversal and the consecutive interior angles on the same side are supplementary, it proves that the lines are parallel. This is based on the Consecutive Interior Angles Converse Theorem.

Explanation:

To prove if two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, we can use the concept of parallel lines and transversal properties.

When the sum of the interior angles on the same side of a transversal is 180 degrees, these angles are called consecutive interior angles, and according to the Consecutive Interior Angles Converse Theorem, this is a condition that guarantees the lines are parallel.

If you have two lines cut by a transversal and the consecutive interior angles are supplementary (add up to 180 degrees), then the lines are definitely parallel. This is because only parallel lines cut by a transversal will produce consecutive interior angles that are supplementary. Thus, if the given angles are supplementary, the lines in question are parallel.

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