The most general renormalizable quantum field theory one can write down for a finite spectrum of spin-0, 1/2, and 1 particles is a gauge theory, with possible spontaneously broken symmetries. The existence of Lie group structures in such a theory is determined by perturbative unitarity of the on-shell scattering amplitudes. Armed with new tools developed for scattering amplitudes, we demonstrate very explicitly how broken symmetries emerge from the constraints of tree unitarity. Such constraints result in relations dictating the couplings to be invariant tensors of the gauge group, and each of these relations has a counterpart for kinematic numerators of on-shell amplitudes. This facilitates the extension of color-kinematics duality to spontaneously broken gauge theories.