Avalanche photodiodes (APDs) have been fabricated in order to determine the impact ionization coefficients of electrons (alpha) and holes (beta) in AlxGa1-xAsySb1-y lattice matched to GaSb for three alloy compositions: (x=0.40, y=0.035), (x=0.55, y=0.045), and (x=0.65, y=0.054). The impact ionization coefficients were calculated from photomultiplication measurements made on specially designed APDs, which allowed for both pure electron and pure hole injection in the same device. Photo-multiplication measurements were made at temperatures ranging from 77K to 300K for all three alloys. A quasi-physical model with an explicit temperature dependence was used to express the impact ionization coefficients as a function of electric-field strength and temperature. For all three alloys, it was found that alpha < beta at any given temperature. In addition, the values of the impact ionization coefficients were found to decrease as the aluminum concentration of the AlGaAsSb alloy was increased. A value between 1.2 and 4.0 was found for beta/x, which is dependent on temperature, alloy composition, and electric-field strength.