Final answer:
Homologous structures are similar features in organisms that were inherited from a common ancestor, while analogous structures are similar due to convergent evolution, not common ancestry. Vestigial structures are remnants of once-functional ancestral traits.
Step-by-step explanation:
Understanding the relationship between different organisms can often be determined by examining structures within them. When considering homologous structures, these are features found in different species that are similar because they were inherited from a common ancestor, regardless of their current function. For example, the hand structure of humans and the paw of a cat both share a similar bone arrangement despite being used for different purposes. In this sense, homologous structures underpin the concept of evolutionary descent from a shared ancestor.
In contrast, analogous structures are those which may look similar or serve similar functions in different species, but do not derive from a common ancestor. This is illustrated when comparing the wings of bats to the wings of butterflies; the similarity arises not from shared ancestry but rather convergent evolution where different species independently evolve similar traits as adaptations to similar environmental challenges.
Vestigial structures are parts of an organism that are reduced in size or have little to no function but are remnants of structures that were functional in the organism's ancestors. Examples of vestigial structures include the pelvic bones in whales or the appendix in humans.
Ultimately, identifying and comparing these structures helps scientists trace the lineage and evolutionary pathways of organisms.