Elementary Geometry for College Students (6th Edition)

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

Chapter 1 - Section 1.6 - Relationships: Perpendicular Lines - Exercises - Page 50: 25

Answer

$\angle TSU+\angle USV=\angle TSV$ $\angle TSV+\angle VSW=\angle TSW$ Therefore, $\angle TSU+\angle USV+\angle VSW=\angle TSW$

Work Step by Step

With angles $\angle TSU$ and $\angle USV$, we can use the Segment Addition Postulate: $\angle TSU+\angle USV=\angle TSV$ (as the drawing shows). With angles $\angle TSV$ and $\angle VSW$, we can use the Segment Addition Postulate: $\angle TSV+\angle VSW=\angle TSW$ (as the drawing shows). Using the equations, and substituting $\angle TSV$, we get $\angle TSU+\angle USV+\angle VSW=\angle TSW$. And now, we proved the Extended Angle Addition Property.
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.