1. Priya: I bet if the alternate interior angles are congruent, then the lines will have to be parallel. Han: Really? We know if the lines are parallel then the alternate interior angles are congruent, but I didn't know that it works both ways. Priya: Well, I think so. What if angle ABC and angle BCJ are both 40 degrees? If I draw a line perpendicular to line A/ through point B, I get this triangle. Angle CBX would be 50 degrees because 40+50 = 90. And because the angles of a triangle sum to 180 degrees, angle CXB is 90 degrees. It's also a right angle! Han: Oh! Then line Al and line GJ are both perpendicular to the same line. That's how we constructed parallel lines, by making them both perpendicular to the same line. So lines Al and GJ must be parallel.

a. Label the diagram based on Priya and Han's conversation.

b. Is there something special about 40 degrees? Will any 2 lines cut by a transversal with congruent alternate interior angles, be parallel?​