What is the relation between transresistance and input impedance of a transistor?
The answer is simple if you know how this "transresistance" is defined - and  how the transresistance is related to the transconductance. Remember the corresponding function (and the very popular graph). Then, the relation to the current gain is obviuous.

Let me add, that I do not like this expression at all ("transresistance"=built-in emitter resistance). The reason is simple: It is NOT a built-in emitter resistance. More than that, it is not a "resistance" at all - but, of course, it has the unit V/A=Ohm. 

It relates the voltage between two nodes (B and E) to the current through two other nodes (C and E). So - this relation can be expressed using the small-signal parameter d(Ic)/d(Vbe)=gm (transconductance). And the inverse of gm could be named "transresistance" rm=1/gm. But we should not use the common resistor symbol for 1/gm (because it is not a resistor).   

To answwer your question, remember the definition of rbe=hie and the corresponding graph Ib=f(Vbe). Comparing this function with the above mentioned graph which defines the transconductance gm will give you the answer to your question.