Power supplied by a Thevenin source

$$P_{Thevenin} = V_{Th}^2 \frac{1}{R_{Th}+R_L}$$

Power supplied by its equivalent Norton source

$$\begin{eqnarray}
P_{Norton} & = & I_N^2 \frac{R_{Th} R_L}{R_{Th}+R_L} \\
 & = & \left(\frac{V_{Th}}{R_{Th}}\right)^2 \frac{R_{Th} R_L}{R_{Th}+R_L} \\
 & = & V_{Th}^2 \frac{R_L/R_{Th}}{R_{Th}+R_L}
\end{eqnarray}$$

So power supplied by a Thevenin Source and its equivalent Norton source are equal only when \$R_{Th} = R_L\$.

Is it true or am I missing something?