  In this paper, we study the properties of the (2+1)-dimensional black holes
from the viewpoint of geometrothermodynamics. We show that the Legendre
invariant metric of the (2+1)-dimensional black holes can produce correctly the
behavior of the thermodynamic interaction and phase transition structure of the
corresponding black hole configurations. We find that they are both curved and
the curvature scalar gives the information about the phase transition point.
