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 - 3-3 Proving Lines Parallel - Practice and Problem-Solving Exercises - Page 161: 29


$\angle 2$ is supplementary to $\angle 7$ because this is given. $\angle 2$ is supplementary to $\angle 3$ because of the definition of a linear pair. Because of the Congruent Supplements Theorem, $\angle 7\cong\angle 3$. Therefore, because of the Converse of the Corresponding Angles Theorem, $l\parallel m$.

Work Step by Step

Use properties that relate the measures of the various angles shown to find a relationship that can be applied to one of the theorems that proves that the lines are parallel. Similarly, you could use known properties that show angles 3 and 6 are supplementary and then use the Converse of the Same-Side Interior Angles Postulate to prove lines l and m are parallel.
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