How do fossils provide evidence that suggest that evolution has occurred

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When looking at fossils from a specific animal, with further detail it can be determined if there are any animals that are living now that could possibly be related to each other. For example it can be determined that a elephant was related to the once known mammoths simply because of how similar there bone structure was and the way they looked physically. If elephants were once mammoths then it could be suggested that after a long period of time they evolved to live in warm climate which made them lose their fur and how they became smaller in size.