The statement you provided is a specific case related to the properties of parallel lines and angles formed when lines are cut by a transversal.
The correct name for the theorem stating that if two coplanar lines are cut by a transversal such that the same-side interior angles are supplementary, then the lines are parallel is the Converse of the Same-Side Interior Angles Theorem.
This theorem helps establish the relationship between the angles created by the transversal and the lines' parallelism.
Here’s a quick overview of the terms mentioned:
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Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
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Converse of the Same-Side Interior Angles Theorem: If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel (this is what your statement refers to).
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Same-Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary.
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Converse of the Alternate Interior Angles Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
Therefore, in your case, the answer is Converse of the Same-Side Interior Angles Theorem.