Are the feet of a duck and a frog homologous structures or analogous structures?

Answer 1

In biology, structures are considered to be homologous if both animals have them because they had a recent common ancestor that had that structure. Analagous structures arise because the animals live in similar environments, and solve the problems of living in that environment the same way.
Therefore, since ducks (birds) and frogs (amphibians) do not have a recent common ancestor, and because they both use their feet to travel efficiently through water (and webbing makes swimming more efficient), the structures are analagous.