Thevenin equivalent of circuit with no voltage sources
To find Rth, open circuit all independent current sources, short all independent voltage sources. 
Connect a fictitious 1V source at the open ckt terminal. 
Find the current driven by 1V source. 
If I is the current driven by 1V source, then \$\frac{V}{I} = \frac{1}{I}\$ is the load seen by the voltage source. i.e., Rth.
$$I = I_{Ro} + gv_x$$
vx = voltage across Ro = 1V
$$\implies I = \frac{1}{Ro}+g = \frac{(1+gRo)}{Ro}$$
$$\therefore R_{th} = 1/I = \frac{Ro}{(1+gRo)} $$
To find Vth, go back to the original ckt.



Vth is the voltage drop across Ro which is same as vx.


Write ohms law equation for voltage across Ro
$$(i_s-gv_x)Ro= v_x$$
$$\implies v_x = i_s\frac{Ro}{(1+gRo)} = V_{th}$$