This answer is incomplete. In general, it is the electron group geometry, not the molecular geometry alone, that determines polarity in accorsance with electronegtivity differences. Regarding water, yes, the polarity is partially a product of the O-H polar bond and the resulting dipole, but the two lone pairs on the O not only cause a bent molecular geometry an prevent the O-H bonds from canceling each other out as vectors, but provide a great amount of electron density in the oxygen's area to contribute to the overall dipole. Imagine H2O with one less lone pair (fictional molecule but just imagine). In this case the O-H bonds still do not cancel, but the region of electron density around the O would be less negative simply because half as many electrons occupy this space.
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