what types of structures have the same function but do not share a common ancestry
Convergent evolution Convergent evolution is the independent evolution of similar features in species of different lineages. Convergent evolution creates analogous structures that have similar form or function but were not present in the last common ancestor of those groups. The cladistic term for the same phenomenon is homoplasy. The recurrent evolution of flight is a classic example, as flying insects, birds, pterosaurs, and bats have independently evolved the useful capacity of flight. Functionally similar features that have arisen through convergent evolution are analogous, whereas homologous structures or traits have a common origin but can have dissimilar functions. Bird, bat, and pterosaur wings are analogous structures, but their forelimbs are homologous, sharing an ancestral state despite serving different functions.
Cilium There are two types of cilia: motile cilia and nonmotile, or primary cilia, which typically serve as sensory organelles. In eukaryotes, motile cilia and flagella together make up a group of organelles known as undulipodia.[4] Eukaryotic cilia are structurally identical to eukaryotic flagella, although distinctions are sometimes made according to function and/or length.[5] Biologists have various ideas about how the various flagella may have evolved.