Final answer:
The relationship between AB being perpendicular to PR and AB equaling CD is congruence; this means both AB and CD are equal in length and perpendicular to PR, defining them as congruent segments.
Step-by-step explanation:
The student's question relates to geometric properties and their implications. Given that line segment AB is perpendicular to line PR, and AB is equal in length to line segment CD, the question asks how the perpendicularity of CD to PR relates to the fact that AB = CD. The correct relationship between these geometric properties is that they are congruent (congruence). This implies that if another segment CD is also perpendicular to PR, then AB and CD are both perpendicular to PR and equal in length, which means by definition they are congruent segments. This is not directly related to the Pythagorean theorem, which would be used if we had to calculate the lengths of the sides of a right triangle.