We present the spectral evolution, light curve, and corresponding interpretation for the normal-bright Type Ia Supernova 2005cg discovered by ROTSE-IIIc. The host is a low-luminosity (M_r = -16.75), blue galaxy with strong indications of active star formation and an environment similar to that expected for SNe Ia at high redshifts. Early-time (t ~ -10 days) optical spectra obtained with the HET reveal an asymmetric, triangular-shaped Si II absorption feature at about 6100 AA with a sharp transition to the continuum at a blue shift of about 24,000 km s^-1. By 4 days before maximum, the Si II absorption feature becomes symmetric with smoothly curved sides. Similar Si II profile evolution has previously been observed in other supernovae, and is predicted by some explosion models, but its significance has not been fully recognized. Although the spectra predicted by pure deflagration and delayed detonation models are similar near maximum light, they predict qualitatively different chemical abundances in the outer layers and thus give qualitatively different spectra at the earliest phases. The Si line observed in SN 2005cg at early times requires the presence of burning products at high velocities and the triangular shape is likely to be formed in an extended region of slowly declining Si abundance that characterizes delayed detonation models. The spectra show a high-velocity Ca II IR feature that coincides in velocity space with the Si II cutoff. This supports the interpretation that the Ca II is formed when the outer layers of the SN ejecta sweep up about 5 x 10^-3 M_sun of material within the progenitor system. (Abridged)
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