Question

5 select the correct answer. which sentence states a property or a definition used in the construction of a perpendicular bisector? a. a line that intersects a line segment at an angle of 90° is parallel to the line segment. b. a line that bisects a line segment is necessarily perpendicular to the line segment. c. any two points equidistant from the midpoint of a line segment lie on its perpendicular bisector. d. any point on a perpendicular bisector is equidistant from each endpoint of the line segment.

Explanation:

A perpendicular bisector of a line - segment is a line that is perpendicular to the line - segment and passes through its mid - point. By definition, any point on the perpendicular bisector of a line segment is equidistant from the two endpoints of the line segment. Option A is incorrect because a 90 - degree intersection means perpendicular, not parallel. Option B is incorrect because a bisecting line is not necessarily perpendicular. Option C is incorrect as the key property is about equidistance from endpoints, not from the mid - point.

Answer:

D. Any point on a perpendicular bisector is equidistant from each endpoint of the line segment.