Elementary Geometry for College Students (6th Edition)

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

Chapter 10 - Section 10.2 - Graphs of Linear Equations and Slope - Exercises - Page 451: 43


The slopes of two lines that are parallel to each other is always equal when the lines are not vertical.

Work Step by Step

First, we draw two vertical lines a distance x away from the x-intercept of each line. Since this represents a common transversal, it follows that corresponding angles are congruent. In addition, both vertical lines are drawn the same distance from the x-intercept of each of the two parallel lines, meaning that they have congruent sides. Thus, the two triangles are congruent by ASA. This means that their rise and run are both congruent, meaning that their slopes are also congruent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.