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### Description

The usual unitarity triangles of either the $3\times 3$ CKM quark flavor mixing matrix or the $3\times 3$ PMNS lepton flavor mixing matrix are not fully rephasing-invariant, although their areas are all equal to a half of the corresponding Jarlskog invariant of CP violation. Here we propose the novel "rescaled unitarity triangles" (RUTs), whose sides are completely rephasing-invariant and whose heights are all equal to the Jarlskog invariant, to reconstruct the CKM and PMNS matrices. In particular, we find that these RUT quantities simply appear in the probabilities of neutrino oscillations or in the rates of B-meson decays, and they satisfy an interesting Pythagoras-like theorem. So the latter is very useful to describe CP violation and test the consistency of the CKM and PMNS unitarities in a more straightfroward way.