## Elementary Geometry for College Students (6th Edition)

$MN+NP=MP$ $MP+PQ=MQ$ Therefore, $MN+NP+PQ=MQ$
$M$, $N$ 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.