The indium nearest-neighbor environment in InGaAs thin films damaged by Ar ion implantation has been studied by extended x-ray absorption fine structure spectroscopy. We find that before the material turns amorphous by Ar irradiation, the In-As nearest-neighbor distance remains close to its crystalline value even when the layer is heavily damaged but not entirely amorphous. Once the Ar dose exceeds the threshold for amorphizing the InGaAs layer, the In-As bond distance relaxes to that of pure crystalline InAs. This sudden change in local structure as the material transforms from crystalline to amorphous suggests that the transition is due to simultaneous amorphous nucleation rather than the accumulation and overlapping of isolated amorphous regions. Moreover, this change in the local structure in a ternary alloy can be used as a criterion for determining the crystalline-to-amorphous transition of the alloy.