If two parallel lines are cut by a transversal, what is true about the pair of alternate interior angles?

If two parallel lines are cut by a transversal, what is true about the pair of alternate interior angles?

• A. Congruent
• B. Supplementary
• C. Vertical
• D. Adjacent

Answer: (A)

When a transversal cuts two parallel lines, alternate interior angles are congruent. The two lines being parallel forces the angle the transversal makes with one line to match the angle it makes with the other line on the opposite side between the lines. This is a consequence of the alternate interior angle theorem: each pair of alternate interior angles has the same measure. This isn’t about vertical angles, which occur when two lines cross at a single point, nor about adjacent angles, which share a vertex and a side. It also isn’t about interior angles on the same side of the transversal, which add up to 180 degrees (they’re supplementary). Here, the key idea is that the alternate interior angles are equal due to the parallelism of the two lines.

When a transversal cuts two parallel lines, alternate interior angles are congruent. The two lines being parallel forces the angle the transversal makes with one line to match the angle it makes with the other line on the opposite side between the lines. This is a consequence of the alternate interior angle theorem: each pair of alternate interior angles has the same measure.

This isn’t about vertical angles, which occur when two lines cross at a single point, nor about adjacent angles, which share a vertex and a side. It also isn’t about interior angles on the same side of the transversal, which add up to 180 degrees (they’re supplementary). Here, the key idea is that the alternate interior angles are equal due to the parallelism of the two lines.