Transversal lines are straight lines that intersect two or more other lines at different points. When a transversal crosses parallel lines, it creates several angles, which can be classified into pairs such as corresponding angles, alternate interior angles, and consecutive interior angles. These relationships are important in geometry and help in solving various mathematical problems. In geometry, understanding transversal lines is essential for proving theorems and solving for unknown angles. For example, if two lines are parallel and a transversal crosses them, the properties of the angles formed can be used to determine the measures of the angles involved. This concept is often applied in fields like architecture and engineering.