   Chapter 1.6, Problem 27E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# If there were no understood restriction to lines in a plane in Theorem 1.6.4, the theorem would be false. Explain why the following statement is false: “In space, the perpendicular bisector of a line segment is unique.”

To determine

To explain:

The reason that the given statement is false.

Explanation

Given:

The given statement is,

“In space, the perpendicular bisector of a line segment is unique.”

Calculation:

Assume that a perpendicular l drawn to a plane intersects the plane at point O. Two points P and Q lies on the line l.

PO=OQ

It can be observed that

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