Question

Horizontal and parallel lines m and n are cut by transversal k. At the intersection of lines k and m, the bottom left angle is 50 degrees. At the intersection of lines k and n, the uppercase right angle is 50 degrees.
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

Answer 1

converse of the alternate interior angles theorem

Reason: the bottom-left angle at m and the upper-right angle at n are alternate interior angles. They are congruent (both 50°), so by the converse of the alternate interior angles theorem the lines m and n are parallel.