Roy, try a real simple case.

50 ohm line, 1/2 wavelength long, open circuit, lossless, sinusoidal steady
state, fed with a 1v p-p voltage source.

Everyone will agree there is a standing wave on this line of course.

now, to make everyone happy... in the middle of the line calculate v(t),
i(t), and p(t), these are the standing wave voltage, current, and power.

now, calculate vf(t), if(t),pf(t), vr(t), ir(t), pr(t) at that point, where
the 'f' terms are the forward wave, the 'r' terms are the reflected wave.

compare and comment on the relation between pf, pr, and p.

extra credit:
repeat calculations at the far end of the line. again compare pf, pr, and
p.