Question

which of the following geometric constructions can have a perpendicular bisector? lines segments rays

Explanation:

Step1: Recall the definitions

A line extends infinitely in both directions. A ray has one endpoint and extends infinitely in one direction. A segment has two endpoints.

Step2: Analyze perpendicular bisector concept

A perpendicular bisector of a geometric construction is a line that is perpendicular to the construction and divides it into two equal parts.
For a line, since it extends infinitely, we can't bisect it (find a mid - point as it has no definite length). For a ray, because it has one endpoint and infinite length on one side, we can't bisect it (the infinite part can't be bisected). For a segment, which has two endpoints and a definite length, we can find its mid - point. Then we can construct a line perpendicular to the segment at its mid - point, which is the perpendicular bisector.

Answer:

segments