Average proton parameters in the magnetosheath downstream from the quasi-perpendicular shock (the quasi-perpendicular magnetosheath) for high solar wind dynamic pressure conditions are observed to vary continuously from high-beta, low-temperature anisotropy to low-beta, high-temperature anisotropy. Observations and theory have shown that this inverse correlation is a direct consequence of pitch angle scattering by electromagnetic ion cyclotron (EMIC) waves, which regulate the anisotropy, restoring the plasma toward marginal stability. Although the previously documented spectral characteristics of EMIC waves are not evident downstream of the quasi-parallel bow shock, the inverse anisotropy-beta relation found in the quasi-perpendicular magnetosheath also holds in the quasi-parallel magnetosheath. This indicates that the EMIC instability regulates the ion anisotropy regardless of the shock geometry.