In parallelogram ABCD, diagonals AC and BD intersect at K. If HF is parallel to BD, with H on AD and F on AC, and FA = 40, DF = 2, find the ratio AH/AD.

ABCD is a parallelogram, so its diagonals bisect each other. Let K be the intersection of diagonals AC and BD. Therefore, $AK = KC$.
We are given $HF \parallel BD$. This implies $HF \parallel DK$ and $HF \parallel BK$.

Consider $\triangle ADK$. Since $HF \parallel DK$, by the Proportionality Theorem (or similar triangles $\triangle AHF \sim \triangle ADK$):

We are given $FA = 40$ units and $DF = 2