Dalitz Plot Analysis of $D^0 \rightarrow K^0_S \pi^+ \pi^-$ and $D^0 \rightarrow K^0_S K^+ K^-$

We present a Dalitz plot analysis of the decays $D^0 \rightarrow K^0_S \pi^+ \pi^-$ and $D^0 \rightarrow K^0_S K^+ K^-$ using data collected by the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$ collider at SLAC. The results of this analysis are a critical input for the determination of the Cabibbo-Kobayashi-Maskawa CP-violating phase $\gamma$ using a $D$ Dalitz analysis of $B^\pm \to D^{(*)} K^{(*)\pm}$ decays.