How do homologies provide evidence for the common ancestry different species?

The evolutionary theory predicts and suggests that all the related organisms share a common ancestor or they are derived from a common ancestor.

The evidence provided by studying the homologous structures or similar structures performing the same functions of the organisms provides the clue that all the organism have evolved from a common ancestor. This method of evolution is known as divergent evolution.

Thus, homologies provides the clue for divergent evolution.