Dissociative electron attachment to H₂O and D₂O is studied using the recently developed ion momentum imaging spectrometer. We obtain the kinetic energy distribution and the angular distribution in the entire 2π range in the plane of the electron beam for H⁻ and O⁻ ions at the three well-known resonances. While the results at the first resonance at 6.5 eV are in excellent agreement with existing experimental and theoretical results, the angular distributions of the ions at the second (8.5 eV) and third resonance (11.8 eV) are considerably different from the available data. The angular distribution at 11.8 eV shows a very unique distribution of the H⁻ ions in the backward hemisphere, while that of the O⁻ ions is in the forward hemisphere. Based on our results, we reassign the symmetry of the resonance seen at 8.5 eV as a B₁ state instead of A₁ as believed till now. The kinetic energy distribution of H⁻ at the third resonance clearly indicate three dissociation channels leading to the formation of the OH radical in the ground and first electronically excited state as well as a complete three-body breakup.