Question

ry: concepts and connections (27.0821000) yl ic (spring)
proving lines parallel
assignment active
practice writing proofs and solving problems using converses of the parallel line theorems.
which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?
converse of the corresponding angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem
converse of the alternate exterior angles theorem

Explanation:

The two 50° angles lie on the same side of the transversal \(k\), and are in matching positions relative to lines \(m\) and \(n\). These are corresponding angles, so their congruence justifies that \(m \parallel n\) via the converse of the corresponding angles theorem.

Answer:

converse of the corresponding angles theorem