Which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?

a. converse of the corresponding angles theorem

b. converse of the alternate interior angles theorem

c. converse of the same side interior angles theorem

d. converse of the alternate exterior angles theorem

Answer: Option 'b' is correct.

Step-by-step explanation:

To prove that two lines are parallel when it cut be transversal.

Let m and n are two lines and the lines are cut by transversal k.

Then, if we show that the alternate interior angles are equal, then m and n become parallel to each other.

So, the converse of the alternate interior angles theorem correctly justifies that the lines are parallel when cut by transversal.

Hence, option 'b' is correct.

B) converse of the alternate interior angles theorem

if the alternate interior angles are congruent, the lines are parallel