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Although type Ia supernovae (SNe Ia) are very important in many astrophysical fields, such as cosmology, their explosion mechanisms and progenitor systems still remain unclear. In physics, the relative equivalent width (REW) of the Si ii 635.5 nm absorption feature reflects the velocity interval of the silicon in the SN ejecta, which may then provide constraints on the explosion mechanisms of SNe Ia. In this paper, we divide the SNe Ia into broad-line (BL) and normal-line (NL) subsamples, based on the REW of the Si ii 635.5 nm absorption lines around their maximum lights, and we find that the BL SNe Ia have a dimmer mean brightness than the NL ones, which is possibly a result of their different metallicities. However, based on a pixel statistics study of the environments of the two subsamples, we do not find any significant potential differences in the environments of the BL and NL SNe Ia, which implies that the explosion mechanisms of SNe Ia could be independent of their progenitor populations.