Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 3 - Parallel and Perpendicular Lines - 3-8 Slopes of Parallel and Perpendicular Lines - Practice and Problem-Solving Exercises: 40

Answer

The answer is below.

Work Step by Step

If a line is perpendicular to a given line with slope s, then its slope is -1/s. If another line is also perpendicular to that line, then it must also have a slope of -1/s, by the definition of perpendicular lines. Thus, the two lines have a slope of -1/s, so they have the same slope. If two lines have the same slope, they are parallel, meaning that two lines which are perpendicular to the same line must be parallel to each other.
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