## Geometry: Common Core (15th Edition)

$WV = 6.75$
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 $\overline{YX}$ and $\overline{XV}$ are congruent to $\overline{WY}$, so they all have lengths of $2.25$. Since $\overline{WV}$ is made up of all three segments, we just add the three segments together to find the total length of $WV$: $WV = WY + YX + XV$ Let's plug in what we know: $WV = 2.25 + 2.25 + 2.25$ Add to solve: $WV = 6.75$