When two parallel lines are cut by a transversal, the alternate interior angles are equal.

When two parallel lines are cut by a transversal, the alternate interior angles are equal.

• A. Sometimes true
• B. Cannot be determined.
• C. Always true
• D. Never true

Answer: (C)

When two parallel lines are cut by a transversal, the interior angles on opposite sides of the transversal must match in measure. This happens because the orientation of the parallel lines forces the angle the transversal makes with each line to be the same within the interior region. If you look at the two intersection points, the interior angles on opposite sides of the transversal occupy corresponding positions relative to the lines, and parallel lines ensure those corresponding positions have equal angles. In other words, the parallelism guarantees a consistent tilt of the transversal as it crosses both lines, making the alternate interior angles equal. If the lines weren’t parallel, those interior angles wouldn’t necessarily be equal.

When two parallel lines are cut by a transversal, the interior angles on opposite sides of the transversal must match in measure. This happens because the orientation of the parallel lines forces the angle the transversal makes with each line to be the same within the interior region. If you look at the two intersection points, the interior angles on opposite sides of the transversal occupy corresponding positions relative to the lines, and parallel lines ensure those corresponding positions have equal angles. In other words, the parallelism guarantees a consistent tilt of the transversal as it crosses both lines, making the alternate interior angles equal. If the lines weren’t parallel, those interior angles wouldn’t necessarily be equal.