can someone explain why the forelimbs of a cat, a bat, and a whale would be homologous structures?

Answer 1

There are usually two types of criteria used to determine homology: similarity and congruence.

The first one takes into account overall similarity (same bones in the same position, same nerves, blood vessels, muscles, etc), ontogeny (similar stages of development from the same origins), and body position relative to other elements.
These similarities outweigh the functional differences given by the adaptation of the same limb to different functions (walking, flying, swimming respectively, in this case).

The second criterium is congruence: similarities thought to be homologous are tested against other traits. Cats, bats and whales are placental mammals, and they all share many other characters that suggest their close relationships; thus the hypothesis that their forelimbs are homologous structures agrees with their being mammals, amniotes, tetrapods, lobe-finned fish, and gnathostomates (paired limbs first appeared in the latter).

Answer 2

The bone structure is very similar. All of the above also have "fingers." Most land animals (except invertebrates) have a similar foreleg structure. Some are much more modified than others. The foreleg came from a common ancestor, way far back when animals began to move onto land.
The ancestors of whales were land animals. They returned to the water, and whales today have vestigial hind legs, and their front legs are now pectoral flippers.

Answer 3

As stated they are homologous because they all have a very simlar bone structure and symmetry. It is worth noting that the genes that structure their formation (especially early in development) are also nearly identical.

Answer 4

Hmmm... unless you're one of those creationist / intelligent design cretins, you might posit that there is a common mammalian ancestor for all three species.

Answer 5

They all have the same number of bones, with similar symmetry.

Answer 6

They all have the same bone structure..