If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

• A. They are supplementary
• B. They are equal to corresponding angles
• C. They are vertical angles
• D. They are congruent

Answer: (D)

When two lines are parallel, the angle the transversal makes with each line is preserved as you move from one intersection to the other. Look at the interior angles between the lines that lie on opposite sides of the transversal. At each intersection, the straight-line angles around the crossing sum to 180 degrees, and because the lines are parallel, the angle the transversal creates with one line forces the interior angle on the opposite side to match. In effect, the alternate interior angles end up measuring the same, so they are congruent. This direct relationship is the reason the statement holds true. The other possibilities don’t describe the two angles’ relationship correctly: they aren’t generally supplementary, they aren’t vertical angles (which occur at a single intersection), and while corresponding angles are equal in parallel lines, that fact doesn’t change the correct characterization of the alternate interior pair as congruent.