Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

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