Question

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 mid - point 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:

The perpendicular bisector of a line segment is a line that divides the segment into two equal - length parts and is perpendicular to it. 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 as a 90 - degree intersection means perpendicular, not parallel. Option B is incorrect because a bisecting line isn't necessarily perpendicular. Option C is incorrect as it's the points equidistant from the endpoints, not the mid - point, that lie on the perpendicular bisector.

Answer:

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