Question

If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.



Same-Side Exterior Angles Theorem

Corresponding Angles Postulate

Converse of the Alternate Exterior Angles Theorem

Alternate Exterior Angles Theorem

Answer 1

The statement "If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent" is known as the **Alternate Exterior Angles Theorem**.

Here’s a brief overview of the options provided:

1. **Same-Side Exterior Angles Theorem**: States that if two parallel lines are cut by a transversal, then same-side exterior angles are supplementary (add up to 180 degrees).

2. **Corresponding Angles Postulate**: States that if two parallel lines are cut by a transversal, then corresponding angles are congruent.

3. **Converse of the Alternate Exterior Angles Theorem**: States that if alternate exterior angles are congruent, then the lines cut by the transversal are parallel.

4. **Alternate Exterior Angles Theorem**: This is the correct name for the theorem you mentioned at the beginning, which specifically states that alternate exterior angles are congruent when two parallel lines are cut by a transversal.

So the correct answer to the statement provided is the **Alternate Exterior Angles Theorem**.