While a suitable candidate particle for dark matter (DM) has yet to be discovered, it is possible one will be found by experiments currently investigating physics on the weak scale. If discovered on that energy scale, the dark matter will likely be producible in significant quantities at colliders like the LHC, allowing the properties of and underlying physical model characterizing the dark matter to be precisely determined. I assume that the dark matter will be produced as one of the decay products of a new massive resonance related to physics beyond the Standard Model, and using the energy distributions of the associated visible decay products, develop techniques for determining the symmetry protecting these potential dark matter candidates from decaying into lighter Standard Model (SM) particles and to simultaneously measure the masses of both the dark matter candidate and the particle from which it decays.