  The white dwarf mass-radius relationship is fundamental to modern
astrophysics. It is central to routine estimation of DA white dwarf masses
derived from spectroscopic temperatures and gravities. It is also the basis for
observational determinations of the white dwarf initial-final mass relation.
Nevertheless, definitive and detailed observational confirmations of the
mass-radius relation (MRR) remain elusive due to a lack of sufficiently
accurate white dwarf masses and radii. Current best estimates of masses and
radii allow only broad conclusions about the expected inverse relation between
masses and radii in degenerate stars. In this paper we examine a restricted set
of 12 DA white dwarf binary systems for which accurate (1) trigonometric
parallaxes, (2) spectroscopic effective temperatures and gravities, and (3)
gravitational redshifts are available. We consider these three independent
constraints on mass and radius in comparison with an appropriate evolved MRR
for each star. For the best-determined systems it is found that the DA white
dwarfs conform to evolved theoretical MRRs at the 1-{\sigma} to 2-{\sigma}
level. For the white dwarf 40 Eri B (WD0413-077) we find strong evidence for
the existence of a "thin" hydrogen envelope. For other stars improved
parallaxes will be necessary before meaningful comparisons are possible. For
several systems current parallaxes approach the precision required for the
state-of-the-art mass and radius determinations that will be obtained routinely
from the Gaia mission. It is demonstrated here how these anticipated results
can be used to firmly constrain details of theoretical mass-radius
determinations.
