## Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole

# Chapter 1 - Section 1.6 - Relationships: Perpendicular Lines - Exercises - Page 52: 27

#### Answer

The statement is false, because in space, it is called a bisector plane. Because in space the locus of points that are equidistant from both ends of the line segment, is a plane.

#### Work Step by Step

In a plane, the perpendicular bisector of a line segment is unique. In space, it is called a bisector plane. Because in space the locus of points that are equidistant from both ends of the line segment, is a plane. The plane is constructed of all the perpendicular bisectors of $AB$. We can imagine this, by drawing one of them and rotating it around the midpoint of $AB$.

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