Answer
$TU = 9$
Work Step by Step
Theorem 6-7 states that if three or more parallel lines cut off congruent segments off of a transversal, then they will cut off congruent segments off of any transversal.
We see from the diagram that the transversals line $\overline{PS}$ is cut off in equal segments by the four parallel lines. We can then deduce that lines $VW$ and $TU$ are also transversals that are cut off in congruent segments by the same four parallel lines. We now know that $\overline{XZ}$ and $\overline{ZU}$ are congruent to $\overline{TX}$, so they all have lengths of $3$.
Since $\overline{TU}$ is made up of all three segments, we just add the three segments together to find the total length of $TU$:
$TU = TX + XZ + ZU$
Let's plug in what we know:
$TU = 3 + 3 + 3$
Add to solve:
$TU = 9$
