AnalogiesElvis impersonators have many similarities, such as long black sideburns and rhinestone-studded suits, that are not inherited. In the same way, biological similarites are not always due to inheritance.
For example, look at the skulls below. They both belong to extinct animals, and in each the upper canine teeth have evolved into long, curving saberteeth with serrated edges. Would you guess that these saberteeth are homologous inherited from a common ancestor with extra-long saberteeth?
Thylacosmilus is more closely related to other marsupials such as kangaroos and koalas than it is to Smilodon. Smilodon is more closely related to other placentals such as housecats and elephants than it is to Thylacosmilus. Saberteeth is not a common trait in the marsupials closely related to Thylacosmilus, or the placentals closely related to Smilodon. Their common ancestor certainly had canine teeth, but they were probably not adapted into fierce "sabers."
As they weren't inherited from a common ancestor, the saberteeth in Smilodon and Thylacosmilus evolved independently from one another. That means that the evolution of saberteeth occurred more than once. One lineage on one part of the tree of life evolved saberteeth from normal length teeth, and a different lineage somewhere else on the tree also evolved saberteeth from normal length teeth.
These saberteeth are analogous structures.
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Thylacosmilus skull photo © Field Museum of Natural History; Smilodon skull photo © University of California Museum of Paleontology
Understanding Evolution © 2020 by The University of California Museum of Paleontology, Berkeley, and the Regents of the University of California