Chapter 1.6, Problem 27E

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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*.

It can be observed that

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