Elementary Geometry for College Students (7th Edition) Clone

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: 23

Answer

$MN+NP=MP$ $MP+PQ=MQ$ Therefore, $MN+NP+PQ=MQ$

Work Step by Step

$M$, $N$ and $P$ are collinear, so because of the Segment Addition Postulate $MN+NP=MP$ (as the drawing shows). $M$, $P$ and $Q$ are also collinear, so because of the Segment Addition Postulate $MP+PQ=MQ$ (as the drawing shows). Using the equations, and substituing $MP$, we get $MN+NP+PQ=MQ$. And now, we proved the Extended Segment Addition Property.
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