It's definitely not rude of course, the aim of chess game is to checkmate, although it takes 10 minutes...
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If your position is completely toast and you don't have anything sufficient but watch your opponent win, please resign! I think it is just rude to do it because it clearly wastes time for both players and can sometimes be annoying to other players who are in the same tournament.
(If all you have left is a king and I have enough dynamite to blow you away, please don't try and resisting with the king by moving as close as possible. It just annoys me)