  We study the module categories of a tilted algebra C and the corresponding
cluster-tilted algebra B. We investigate how various properties of a C-module
are affected when considered in the module category of B. We give a complete
classification of the projective dimension of a C-module inside the module
category of B. If a C-module M is rigid, we show two sufficient conditions for
M to be a rigid B-module. In particular, if M is an indecomposable and rigid
C-module, we prove M is always a rigid B-module.
