In a tennis court, the center line divides the court into two equal halves, and it is perpendicular to both service lines. To explain why the service lines must be parallel to each other, we can refer to a fundamental concept in Euclidean geometry called the Converse of the Corresponding Angles Postulate.
The Converse of the Corresponding Angles Postulate states that if a pair of corresponding angles formed by a transversal and two lines are congruent (equal in measure), then the two lines are parallel. In the context of a tennis court, the center line acts as a transversal that intersects both service lines.
As the center line is perpendicular to both service lines, it forms a right angle (90 degrees) with each of them. These right angles are corresponding angles, and since they are both equal in measure (90 degrees), according to the Converse of the Corresponding Angles Postulate, the service lines must be parallel to each other.