Final answer:
Comparing DNA sequences to determine a shared evolutionary history is called phylogenetic analysis, which uses DNA similarities to infer evolutionary relationships and construct phylogenetic trees.
Step-by-step explanation:
Comparing DNA sequences to find evidence of a shared evolutionary history is called phylogenetic analysis. The similarities in DNA sequences are a significant indicator of common ancestry among species. The more similar the DNA sequences are between two organisms, the closer their evolutionary relationship is likely to be.
Through the use of computational tools like sequence alignment and databases such as GenBank, as well as software like BLAST (basic local alignment search tool), scientists can compare the DNA sequences of different organisms. These comparisons help construct phylogenetic trees which represent the evolutionary links between species. It's important to distinguish between homologous and analogous characteristics to accurately infer these relationships, as homologous traits support divergent evolution and denote a closer genetic kinship.