  We present an investigation of the properties of the extended Ly$\alpha$ halo
and the large-scale \ion{H}{I} absorbing structures associated with 5
high-redshift radio galaxies at z $>$ 2, using the Goodman long-slit
spectrograph on the SOAR telescope, with the slit placed at large angles
($>$45$^{\circ}$) to the radio axis, to study regions that are unlikely to be
illuminated by the active nucleus. Spatially extended Ly$\alpha$ emission is
detected with large line widths (FWHM = 1000 -- 2500 km s$^{-1}$), which
although impacted by resonant scattering, is suggestive of turbulent motion. We
find a correlation between higher blueshifts and higher FWHM, which is an
indication that radial motion dominates the bulk gas dynamics perpendicular to
the radio axis, although we are unable to distinguish between outflow and
infall scenarios due to the resonant nature of the Ly$\alpha$ line. Extended,
blueshifted Ly$\alpha$ absorption is detected in the direction perpendicular to
the radio axis in three radio galaxies with minimum spatial extents ranging
from $\gtrsim$27 kpc to $\gtrsim$35 kpc, supporting the idea that the absorbing
structure covers the entire Ly$\alpha$ halo, consistent with being part of a
giant, expanding shell of gas enveloping the galaxy and its (detected) gaseous
halo.
