Field line resonances (FLRs) are important for transferring energy from fast mode waves to shear Alfvén waves in the Earth's magnetosphere. Using simultaneous multi-satellite observations from THEMIS and the IMAGE ground magnetometer array, we report on the transfer of energy from compressional magnetopause undulations through an FLR to the ionosphere. Energy diversion from the magnetosphere to the ionosphere took place at the FLR: we find net energy flux there to have comparable values in the radial and the field-aligned directions. The field-aligned energy flux, when mapped to the ionosphere, was 0.70 mW/m2 and consistent with the inferred Joule dissipation rate at that time. IMAGE's regional monitoring of wave activity reveals that the temporal evolution of the FLR wave power and energy transfer were correlated with the amplitude profile of magnetopause undulations, confirming these waves to be the FLR driver.