Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 2 - Section 2.1 - The Parallel Postulate and Special Angles - Exercises - Page 75: 18


CA is not parallel to BE

Work Step by Step

The three dimensional figure shown depicts CA perpendicular to AB perpendicular to BE. If these line segments were all in the same plane, then CA would be parallel to BE. However, in the diagram, CA and BE are $not$ on the same plane. According to the definition of parallel lines (in Euclidean geometry), they $must$ be on the same plane . Since they are not, CA is not parallel to BE.
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