A monster with human head and lions body that gave riddles to travelers?

The Sphinx, a creature with the body and legs of a lion, a great bird's wings and the head of a woman, terrorized the city of Thebes. It would ask a riddle and then devour anyone who couldn't answer it. Oedipus answered the riddle, driving the Sphinx mad so that it flung itself from a rock and was destroyed...

Which was weird since the thing had wings and could have flown.