  It is well known that interpreting the cosmological constant as the pressure,
the AdS black holes behave as the van der Waals thermodynamic system. In this
case, like a phase transition from vapor to liquid in a usual van der Waals
system, black holes also changes phases about a critical point in the $P$-$V$
picture, where $P$ is the pressure and $V$ is the thermodynamic volume. Here,
we give a geometrical description of this phase transition. Defining the
relevant Legendre invariant thermogeometrics corresponding to the two
criticality conditions, which determine the critical values of respective
thermodynamical entities, we show that the critical point refers to the
divergence of the Ricci scalars calculated from these metrics. The similar
descriptions are also provided for the other two pictures of the van der Waals
like phase transition: one is $T$-$S$ and the other one is $Y$-$X$ where $T$,
$S$, $X$ and $Y$ are temperature, entropy, generalized force and generalized
displacement; i.e. potential corresponding to external charge, respectively.
The whole discussion is very general as no specific black hole metric is being
used.
