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: 22

Answer

The given statement is false because lines can have infinite other lines perpendicular to the infinitely many points on said line.

Work Step by Step

The Given Statement (which had to be explained false as the answer): "In space, there is exactly one line perpendicular to a given line at any point on the line." In simpler terms, there is only 1 line perpendicular to another line, no matter what. This is false because, in reality, there are infinitely many lines perpendicular to a line. For every point on a line, there is one line perpendicular to it which runs through that point. Since there are infinitely many points on a line, there are infinitely many lines which are each perpendicular to a different point on said line.
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