Recent experimental results concerning reactive scattering in the hyperthermal kinetic energy regime can be described by energy scaling relationships E(i) cos(n) theta(i), where n<2, and E(i) and theta(i) are the incident kinetic energy and incident angle, respectively. Such power law scaling arguments are empirical, the results of which cannot easily be related to the fundamental parameters that describe the gas-surface interaction. We present a detailed and thorough analysis where the role of surface corrugation in determining the coupling between incident kinetic energy and incident angle in these translationally activated systems is considered explicitly. The key features of the analysis involve the assumption that the kinetic energy directed along the local surface normal (E(perpendicular to)) controls the reaction probability (S-R), and that by averaging this quantity over the unit cell, one obtains the appropriate energy scaling relationship. The major advantage associated with the proposed analysis is that one need not assume a functional form concerning how the reaction probability depends on kinetic energy, i.e., S-R(E(perpendicular to)). Our analysis demonstrates that in the absence of shadowing, a single "universal" scaling function exists E(i) theta(theta(i)), which is given by the expression theta(theta(i))=(1-Delta)cos(2) theta(i)+3 Delta sin(2) theta(i), where Delta is a corrugation parameter (0 less than or equal to Delta less than or equal to 1) and only in-plane corrugation has been considered. Shadowing plays an important role at sufficiently large corrugation amplitudes and/or sufficiently large angles of incidence. Specifically, it leads to more complex scaling functions, which depend on the shape of the surface corrugation, for which several examples have been considered. Both local minima and local maxima can be observed for theta(theta(i)) as a function of incident angle. Two factors can introduce errors in the analysis, namely, the presence of nonlinearities, and the effects of nonuniform surface reactivity, and illustrative examples are considered. The model accounts well for recent experimental results concerning the dissociation of silanes on silicon surfaces, and alkanes on a corrugated platinum surface. It is probable that other systems involving reactive scattering in the hyperthermal kinetic energy regime may also be described well employing this analysis.