We present a detailed spectroscopic and photometric analysis of 219 DA and DB white dwarfs for which trigonometric parallax measurements are available. Our aim is to compare the physical parameters derived from the spectroscopic and photometric techniques, and then to test the theoretical mass-radius relation for white dwarfs using these results. The agreement between spectroscopic and photometric parameters is found to be excellent, especially for effective temperatures, showing that our model atmospheres and fitting procedures provide an accurate, internally consistent analysis. The values of surface gravity and solid angle obtained, respectively, from spectroscopy and photometry, are combined with parallax measurements in various ways to study the validity of the mass-radius relation from an empirical point of view. After a thorough examination of our results, we find that 73% and 92% of the white dwarfs are consistent within 1{sigma} and 2{sigma} confidence levels, respectively, with the predictions of the mass-radius relation, thus providing strong support to the theory of stellar degeneracy. Our analysis also allows us to identify 15 stars that are better interpreted in terms of unresolved double degenerate binaries. Atmospheric parameters for both components in these binary systems are obtained using a novel approach. We further identify a few white dwarfs that are possibly composed of an iron core rather than a carbon/oxygen core, since they are consistent with Fe-core evolutionary models.