  We present a detailed spectroscopic and photometric analysis of DA and DB
white dwarfs drawn from the Sloan Digital Sky Survey with trigonometric
parallax measurements available from the Gaia mission. The temperature and mass
scales obtained from fits to $ugriz$ photometry appear reasonable for both DA
and DB stars, with almost identical mean masses of $\langle M \rangle =
0.617~M_\odot$ and $0.620~M_\odot$, respectively. The comparison with similar
results obtained from spectroscopy reveals several problems with our model
spectra for both pure hydrogen and pure helium compositions. In particular, we
find that the spectroscopic temperatures of DA stars exceed the photometric
values by $\sim$10% above $T_{\rm eff}\sim14,000$~K, while for DB white dwarfs,
we observe large differences between photometric and spectroscopic masses below
$T_{\rm eff}\sim16,000$~K. We attribute these discrepancies to the inaccurate
treatment of Stark and van der Waals broadening in our model spectra,
respectively. Despite these problems, the mean masses derived from spectroscopy
--- $\langle M \rangle = 0.615~M_\odot$ and $0.625~M_\odot$ for the DA and DB
stars, respectively --- agree extremely well with those obtained from
photometry. Our analysis also reveals the presence of several unresolved double
degenerate binaries, including DA+DA, DB+DB, DA+DB, and even DA+DC systems. We
finally take advantage of the Gaia parallaxes to test the theoretical
mass-radius relation for white dwarfs. We find that 65% of the white dwarfs are
consistent within the 1$\sigma$ confidence level with the predictions of the
mass-radius relation, thus providing strong support to the theory of stellar
degeneracy.
