Question

If two coplanar lines are cut by a transversal so that same-side interior angles are supplementary, then the lines are parallel.



Alternate Interior Angles Theorem

Converse of the Same-Side Interior Angles Theorem

Same-Side Interior Angles Theorem

Converse of the Alternate Interior Angles Theorem

Answer 1

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:

- **Alternate Interior Angles Theorem**: If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

- **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).

- **Same-Side Interior Angles Theorem**: If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary.

- **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**.