  We study the extended phase space thermodynamics of black holes in massive
gravity. Particularly, we examine the critical behaviour of this black hole
using the extended phase space formalism. Extended phase space in a sense that
in which the cosmological constant should be treated as a thermodynamic
pressure and its conjugate variable as a thermodynamic volume. In this phase
space, we derive the black hole equation of state, the critical pressure, the
critical volume and the critical temperature at the critical point. We also
derive the critical ratio of this black hole. Moreover, we derive the black
hole reduced equation of state in terms of the reduced pressure, the reduced
volume and the reduced temperature. Furthermore, we examine the Ehrenfest
equations of black holes in massive gravity in the extended phase space at the
critical point. We show that the Ehrenfest equations are satisfied of this
black hole and the black hole encounters a second order phase transition at the
critical point in the said phase space. This is re-examined by evaluating the
Pregogine-Defay ratio~($\varPi$). We determine the value of this ratio is
$\varPi=1$. The outcome of this study is completely analogous to the nature of
liquid-gas phase transition at the critical point. This investigation also
further gives us the profound understanding between the black hole of massive
gravity with the liquid-gas system.
