  The $\gamma$ decays of the Isovector Giant Dipole Resonance (GDR) of the
deformed nucleus $^{154}$Sm from $2^+_1$-Smekal-Raman and elastic scattering
were measured using linearly polarized, quasi-monochromatic photon beams. The
two scattering processes were disentangled through their distinct angular
distributions. Their branching ratio and cross sections were determined at six
excitation energies covering the $^{154}$Sm GDR. Both agree with the
predictions of the geometrical model for the GDR and establish $\gamma$ decay
as an observable sensitive to the structure of the resonance. Consequently, the
data place strong constraints on the nuclear shape, including the degree of
triaxiality. The derived $^{154}$Sm shape parameters $\beta=0.2926(26)$ and
$\gamma=5.0(14)$ agree well with other measurements and recent Monte Carlo
Shell-Model calculations.
