## Geometry: Common Core (15th Edition)

$ED = 12$ $FD = 24$
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 transversal $\overline{AC}$ is cut off in equal segments by the three parallel lines. We can then deduce that line $DF$ is also a transversal that is cut off in congruent segments by the same three parallel lines. We now know that $ED$ is congruent to $FE$, so they both have a length of $12$. We are asked to find the length of $\overline{FD}$. We can do this by adding the lengths of the two segments together: $FD = FE + ED$ Let's plug in what we know: $FD = 12 + 12$ Add to solve for $FD$: $FD = 24$