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.
