Lesson 20 Practice Problems
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
draw a line perpendicular to line AI 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 AI 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 AI and GJ must be parallel.
F
A
G
C40°
40°
B
X
E
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?