Comparative biochemistry is the study of the arrangement of molecules in organisms. Comparative biochemists may study the amino acid sequences in proteins, the nucleotide sequences in DNA and RNA, and may try to obtain DNA from fossils for comparison with living organisms. Both comparative morphology and comparative biochemistry can be used to study divergence and convergence, the two major types of evolutionary change. In divergence, organisms that share a common ancestor become more different with the passage of generations. In convergence, organisms that do not share a recent common ancestor become more similar.
Divergence is much more common than convergence.
Organisms typically more different with the passage of time. The degree of difference can be used to estimate the closeness of the relationship. A famous example is the evolutionary history of the vertebrate forelimb, which is beautifully depicted in your textbook. A famous example from the vertebrates is the similar body and fin shape of sharks, porpoises, and penguins. An example of covnergence shown on a slide during lecture is the development of wings by insects and birds, which are not particularly closely related types of animals.