  The 3 X 3 CKM matrix defines six unitarity triangles in the complex plane,
which will be carefully explored in the LHCb experiment and at the Super-B
factory. We calculate the running effects of nine different inner angles and
eighteen different sides of the six triangles from the electroweak scale to a
superhigh-energy scale by using the one-loop renormalization-group equations,
and demonstrate that all the nine angles are stable against radiative
corrections. In particular, we find that the CP-violating angle \alpha is most
insensitive to the changes of energy scales.
