What is true about angles formed when parallel lines are cut by a transversal?

When parallel lines are intersected by a transversal, a variety of angle relationships emerge. The statement that alternate interior angles are equal accurately captures one of these key relationships.

When one transversal crosses parallel lines, it creates pairs of alternate interior angles that lie on opposite sides of the transversal and inside the parallel lines. Due to the parallel nature of the lines, the alternate interior angles maintain equality. This means if you measure one angle, its alternate interior counterpart will have the same degree measure.

This property is a fundamental aspect of parallel line geometry and is often utilized in proofs and problem-solving related to angles, helping to establish angle relationships in various geometric scenarios. Understanding this concept is crucial for solving many geometry problems involving parallel lines and transversals.