Step 1: Use the power perspective for matched load.
A matched load means $Z_L = Z_0$. When no impedance discontinuity exists, the wave traveling toward the load encounters no change in impedance. By energy conservation, all incident power must be absorbed by the load.
Step 2: Compute the reflection coefficient from power.
Reflected power $P_r = |\Gamma|^2 \cdot P_i$. Since no power is reflected ($P_r = 0$): $|\Gamma|^2 = 0 \Rightarrow |\Gamma| = 0$.
Step 3: Derive VSWR from reflection coefficient.
$VSWR = \dfrac{1 + |\Gamma|}{1 - |\Gamma|} = \dfrac{1+0}{1-0} = 1$. A VSWR of 1 means a perfectly flat voltage distribution on the line. \[ \boxed{VSWR = 1,\;\Gamma = 0} \]