Problem

Parallel lines are cut by a transversal, and \(\text{two}~\text{angles}\) occupy matching corners. Name the angle theorem that applies and state the congruence relationship it guarantees.

Unworked line or perpendicular-bisector configuration showing only supplied evidence.

Big Picture

What this problem is really about

The quickest theorem check is to separate what is already known from what must be concluded. We’ll use the given parallelism to establish the forward direction, classify the two marked regions by their matching corners at separate intersections, and then state the angle relationship that follows.

Answer choices

Choose your path.

Preview only

This is the corresponding angles theorem, because angles in matching corners on parallel lines cut by a transversal are congruent.

This is the converse of the alternate interior angles theorem, because equal-looking angle pairs can be used to show the lines are parallel.

This is the vertical angles theorem, because the angles are across from each other where the lines intersect.

This is the same-side interior angles theorem, because angles made by a transversal with parallel lines always add to 180 degrees.

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Parallel lines are cut by a transversal, and \(\text{two}~\text{angles}\) occupy matching corners. Name the angle theorem that applies and state the congruence relationship it guarantees.

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.