Materials showing rapid intramolecular energy transfer and polarization switching are of interest for both their fundamental photophysics and potential for use in real-world applications. Here we report two donor-acceptor-donor triad dyes based on perylene-bisimide subunits, with the long axis of the donors arranged either parallel or perpendicular to that of the central acceptor. We observe rapid energy transfer ($<$ 2\,ps) and effective polarization control in both dye molecules in solution. A distributed-dipole F\"{o}rster model predicts the excitation energy transfer rate for the linearly arranged triad, but severely underestimates it for the orthogonal case. We show that the rapid energy transfer arises from a combination of through-bond coupling and through-space transfer between donor and acceptor units. As they allow energy cascading to an excited state with controllable polarization, these triad dyes show high potential for use in luminescent solar concentrator devices.