How are Odysseus and Penelope alike?
In The Odyssey, Homer's epic classic of courage and strength, the subjects of your question are the main characters.
Odysseus is the hero of the story, and in the classic style he is a man with the qualities of strength, skill, determination, moral responsibility, intelligence, loyalty and adaptability. All of these qualities come into play in his adventures from the time he leaves home until his return.
Penelope, his wife who is left behind in less than ideal circumstances, is stronger than any other female character of the time. She too demonstrates many ideals that surface during the struggles she faces - strength, courage, moral strength, intelligence, loyalty, etc... Most of these are evidenced in her handling of her suitors when it appears that her husband will not return.
That being said, the similarities that stand out the most seem to be in the areas of strength, moral responsibility, intelligence and loyalty.