"In the next land we found were Cyclopes, giants, louts, without a law to bless them" (L.56-57, Pg.374).
"If I killed him we perished there as well, for we could never move his ponderous doorway slab aside" (L.207-209, Pg.378).
Odysseus getting trapped by the Cyclops
Odysseus is giving the Cyclops wine
"Cyclops, try some wine" (L.256, Pg.379).
Odysseus arriving to the Cyclops proves he is an epic hero because he is traveling outside his own village. If you travel outside of your village that means you are brave and are willing to take scary chances.
Odysseus following through with the plan on how to escape
"Nohbdy, nohbdy's tricked me, Nohbdy's ruined me" (L.318, Pg.381)!
While Odysseus was getting trapped by the Cyclops, he was also thinking ahead on how to get out and at the same time comforting the men. This shows that he is an epic hero because while something bad was happening he was still pushing through.
Odysseus using the Cyclops to his advantage
Odysseus giving the Cyclops wine is an example of him being a epic hero because he knows that the wine will make Polyphemus drunk and he will fall asleep, so they can follow through with their plan.
Odysseus getting away
"So we moved out, sad in the vast offing, having our precious lives, but not our friends" (L.483-485, Pg.385).
When the Cyclops was sound asleep, Odysseus stabbed him in the eye with a adze to make him blind. Even though the Cyclops screams for help, because Odysseus has told him his name was "nobody," when the other Cyclopes ask who is hurting Polyphemus, he answers, "nobody." So they figure noting is wrong. This proves that Odysseus is a epic hero because he thought the plan through on how to escape and on how to get away with it.
Odysseus and all of his men strapped themselves on the undersides of the rams. This way, Polyphemus only feels the fleece of the rams not the men as they escape. This shows that Odysseus in a epic hero because he got most of his men out safe and still got away from the Cyclops.
"I took the woolliest ram, the choicest of the flock, and hung myself under his kinky belly..." (L.441-433, Pg.381).
Odysseus and his men finally got back to thier boat, most of them made it. This proves that Odysseus is a epic hero because even though he didn't know the Cyclops were going to lock them up, he still found a way to get his men out of the trap with a well thought out plan.