Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 1 - Section 1.6 - Relationships: Perpendicular Lines - Exercises: 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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