Similar symbioses have evolved again and again in plants and animals. Paramecium sometimes houses photosynthetic algae, corals contain photosynthetic dinoflagellates, and termite endosymbionts are eukaryiotic cells associated with prokaryotic bacteria that wave like flagellae. Then relate these to the definitions of analogy, ancestral homology, and derived homology. Characters that have become similar through convergent evolution are called analogies. These are not good characters for classification, because grouping by analogies creates polyphyletic groups.
Homologies are characters that are similar because of common ancestry.
Shared derived homologies are those where the common ancestor and all of its descendants share the same character state. Shared ancestral homologies are those where the common ancestor and only some of its descendents have the same character state.