Theorems about parallel lines focus on the relationships between angles formed when a transversal crosses two parallel lines. One key theorem states that corresponding angles are equal. This means if two parallel lines are cut by a transversal, the angles in matching corners are the same. Another important theorem is the Alternate Interior Angles Theorem, which states that the pairs of angles on opposite sides of the transversal but inside the parallel lines are also equal. These theorems help in understanding geometric properties and are fundamental in proving other geometric concepts involving angles and lines.