Final answer:
In the case of two parallel lines cut by a transversal, corresponding angles on the same side of the transversal are congruent. They will have the same measure.
Step-by-step explanation:
The relationship between a pair of angles that are on the same side of a transversal and between the parallel lines is that they are congruent. This can be summarized by the term corresponding angles, which states that in such a situation, the angles are equal. This property is a result of Euclidean geometry and is fundamental in the study of geometry and trigonometry.
For example, if two parallel lines are cut by a transversal, the angles in matching corners, such as the top right angle on the first line and the top right angle on the second line, would both be equal. Similarly, the bottom left angle on the first line and the bottom left angle on the second line would also be congruent. Hence, if one of the corresponding angles were 60 degrees, the other would also be 60 degrees.