Final answer:
Two parallel lines cut by a transversal result in corresponding angles being congruent and interior angles on the same side of the transversal being supplementary. These principles help in solving geometric problems and proving theories.
Step-by-step explanation:
When two parallel lines are cut by a transversal, several pairs of angles are formed. One key property is that corresponding angles are congruent. Corresponding angles are those that are located at the same position at each intersection where the transversal crosses the parallel lines. They are equal in measure, thus making statement B true.
Another important property is that each pair of interior angles on the same side of the transversal are supplementary, which means their measures add up to 180 degrees. This is also known as the Consecutive Interior Angles Theorem, confirming that statement C is true. These relationships help establish important principles in geometry, such as the basis for proving two lines are parallel or for solving for unknown angles within a network of lines.
Using these angle relationships is fundamental for understanding geometry, solving problems involving angles, and proving more complex geometric theorems. Therefore, when two parallel lines are cut by a transversal, it's important to identify these angle pairs and apply the corresponding principles accordingly.