  We propose a new query application for the well-known Trapezoidal Search DAG
(TSD) of a set of $n$~line segments in the plane, where queries are allowed to
be {\em vertical line segments}.
  We show that a simple Depth-First Search reports the $k$ trapezoids that are
intersected by the query segment in $O(k+\log n)$ expected time, regardless of
the spatial location of the query. This bound is optimal and matches known data
structures with $O(n)$ size. In the important case of edges from a connected,
planar graph, our simplistic approach yields an expected $O(n \log^*\!n)$
construction time, which improves on the construction time of known structures
for vertical segment-queries. Also for connected input, a simple extension
allows the TSD approach to directly answer axis-aligned window-queries in $O(k
+ \log n)$ expected time, where $k$ is the result size.
