Question

Are bird wings and the wings of bats (evolved from limbs) an example of an evolutionary homology or analogy?  What about whale fins compared to fish fins?

Answer 1

Analogy or analogous structure, is actually the one that doesn't indicate that there is a recent common ancestors between two organisms. They are actually a product of convergent evolution, while homology means the two organisms have evolved from common ancestors but they vary in structure and function due to lived in different environment and it is a example of divergent evolution.

For example, the wings of birds and bats are analogous because they are structurally different but the wings are used for similar function.

Just like the above example, the whale is a mammal. Both whale and fish, live in similar environment in the ocean where fins are favorable adaptations for animals needs to swim and move in the water. But they wouldn't have common ancestors and therefore the fins of whale and fish are considered to be analogous structure.