We compare the morphology of active region structures observed in the 171 Å (T~9×105 K) and Lyα (T~2×104 K) lines. The coronal data were obtained by the Transition Region and Coronal Explorer (TRACE) in support of the Very High Angular Resolution Ultraviolet Telescope (VAULT) sounding rocket launch, which acquired subarcsecond resolution images of an active region in the Lyα line, on 1999 May 7. Using a pair of calibrated, nearly simultaneous images, we find that: (i) a very good correlation exists between the Lyα and 171 Å intensities in the TRACE moss regions, (ii) we can identify several identical structures in some (but not all) moss areas, and (iii) the correlations are greatly reduced at the footpoints of the 171 Å large-scale loops. We derive a lower limit for the Lyα emission measure, under the assumption of effectively optically thin emission, and compare it to the 171 Å emission measure. As in previous studies, we find an excess of Lyα material compared to the amount expected for a thermal conduction-dominated corona-chromosphere transition region, even for structures that appear to be identical in the two wavelengths. This result implies that some other mechanism besides classical heat conduction from the corona must contribute to the observed Lyα intensities. The observations do not support the idea of a physically distinct cool loop component within active regions.