We present spectroscopic observations from the {it Spitzer Space Telescope} of six carbon-rich AGB stars in the Sagittarius Dwarf Spheroidal Galaxy (Sgr dSph) and two foreground Galactic carbon stars. The band strengths of the observed C$_2$H$_2$ and SiC features are very similar to those observed in Galactic AGB stars. The metallicities are estimated from an empirical relation between the acetylene optical depth and the strength of the SiC feature. The metallicities are higher than those of the LMC, and close to Galactic values. While the high metallicity could imply an age of around 1 Gyr, for the dusty AGB stars, the pulsation periods suggest ages in excess of 2 or 3 Gyr. We fit the spectra of the observed stars using the DUSTY radiative transfer model and determine their dust mass-loss rates to be in the range 1.0--3.3$times 10^{-8} $M$_{odot}$yr$^{-1}$. The two Galactic foreground carbon-rich AGB stars are located at the far side of the solar circle, beyond the Galactic Centre. One of these two stars show the strongest SiC feature in our present Local Group sample.
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