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: 40

Answer

(a) $\overline{AG}$ and $\overline{BC}$ are skew line segments. (b) $\overline{AG}$ and $\overline{BC}$ are not congruent line segments. (c) $\overline{GF}$ and $\overline{DC}$ are parallel.

Work Step by Step

(a) $\overline{AG}$ and $\overline{BC}$ are not parallel and they do not intersect. Therefore $\overline{AG}$ and $\overline{BC}$ are skew line segments. (b) $\overline{BC}$ appears to be longer than $\overline{AG}$. That is, $\overline{AG}$ and $\overline{BC}$ do not have the same length. Therefore $\overline{AG}$ and $\overline{BC}$ are not congruent line segments. (c) $\overline{GF}$ and $\overline{AB}$ are on opposite sides of a rectangle. Therefore $\overline{GF}$ and $\overline{AB}$ are parallel. $\overline{AB}$ and $\overline{DC}$ are on opposite sides of a rectangle. Therefore $\overline{AB}$ and $\overline{DC}$ are parallel. Therefore, $\overline{GF}$ and $\overline{DC}$ are parallel.
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