Intuition on Thevenin's Theorem
The Thevenin equivalent is not a closed circuit, it will have an output node. So the final Thevenin circuit will be Vth in series with R3, whose other terminal will connect to the rest of the circuit. 

It does not matter what components the original circuit used, what matters is what will be the resistance seen at the node, and what will be the voltage without any load. Knowing these two information, the voltage and current at the output can be calculated.

The Thevenin equivalent is not the same circuit, it just looks equivalent FROM the outside word, i.e. looking into the terminals of the circuit. This simplifies so many calculations! It is a very important concept used by every day in analog circuit design.