Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 1 - Section 1.3 - Early Definitions and Postulates - Exercises - Page 28: 39

Answer

(a) $\overline{AB}$ and $\overline{DC}$ are parallel. (b) $\overline{AB}$ and $\overline{FE}$ are skew line segments. (c) $\overline{AB}$ and $\overline{FE}$ are perpendicular.

Work Step by Step

(a) $\overline{AB}$ and $\overline{DC}$ are on opposite sides of a rectangle. Therefore $\overline{AB}$ and $\overline{DC}$ are parallel. (b) $\overline{AB}$ and $\overline{FE}$ are not parallel and they do not intersect. Therefore $\overline{AB}$ and $\overline{FE}$ are skew line segments. (c) $\overline{AB}$ and $\overline{GF}$ are on opposite sides of a rectangle. Therefore $\overline{AB}$ and $\overline{GF}$ are parallel. $\overline{GF}$ and $\overline{FE}$ meet at a right angle. Therefore, $\overline{GF}$ and $\overline{FE}$ are perpendicular. Therefore, $\overline{AB}$ and $\overline{FE}$ are perpendicular.
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