Calculate Triangle and Trapezoid Measurements: Finding Lengths 6, 9, and 4.5

This problem involves identifying the correct similarity ratio of triangles based on given line segments. We have triangle $\triangle ACF$ with line segments $AC$ and $CF$, and triangle $\triangle BDV$ with line segments $BD$ and $DV$, where corresponding side lengths of similar triangles should satisfy proportional relationships.

First, recognize that for similar triangles, the ratio of corresponding sides should be equal. If triangles $\triangle ACF$ and $\triangle BDV$ are similar, the segments would meet certain proportional criteria. The possible ratios could be formed by recognizing:

• $\frac{FV}{AC}$ should correspond to the smaller segment extending from a vertex to base or equivalent in the other triangle setup.
• $\frac{DV}{AB}$ matches up the vertex downward extension similar to $\frac{FV}{AC}$ with a base side.
• $\frac{FD}{BC}$ must be the ratio of a cross-cutting or diagonal side ratio to maintain similarity from base to opposite corner.

Thus, the correct setup for these segments should reflect that:
$\frac{FV}{AC} = \frac{DV}{AB} = \frac{FD}{BC}$

By evaluating each choice given, the correct answer would align with this reasoning. Therefore, the correct choice is: $\frac{FV}{AC} = \frac{DV}{AB} = \frac{FD}{BC}$.