Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 1 - Section 1.4 - Relationships: Perpendicular Lines - Exercises - Page 62: 25


$\angle TSU+\angle USV=\angle TSV$ $\angle TSV+\angle VSW=\angle TSW$ 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.
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