Final answer:
The Lotus-Eaters pose a danger to Odysseus' men by offering them the Lotus plant, causing them to lose interest in returning home.
Step-by-step explanation:
The danger that the Lotus-Eaters pose to Odysseus' men in the excerpt from the Odyssey, Part 1 is that they offer the men the Lotus plant, causing them to lose interest in returning home. The Lotus plant has a narcotic effect, making those who consume it forget their purpose and desire only to stay and consume more. This poses a danger to Odysseus' men as it distracts them from their goal of returning home.
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