Evolutionary theory predicts that related organisms will share similarities that are derived from common ancestors. Similar characteristics due to relatedness are known as homologies. Homologies can be revealed by comparing the anatomies of different living things, looking at cellular similarities and differences, studying embryological development, and studying vestigial structures within individual organisms.
In the following photos of plants, the leaves are quite
different from the "normal" leaves we envision.
Each leaf has a
very different shape and function, yet all are homologous structures,
derived from a common ancestral form. The pitcher plant and Venus' flytrap
use leaves to trap and digest insects. The bright red leaves of the poinsettia
look like flower petals. The cactus leaves are modified
into small spines which reduce water loss and can protect the cactus
Another example of homology is the forelimb of tetrapods (vertebrates with legs).
Frogs, birds, rabbits and lizards all have different forelimbs, reflecting their different lifestyles. But those different forelimbs all share the same set of bones - the humerus, the radius, and the ulna. These are the same bones seen in fossils of the extinct transitional animal, Eusthenopteron, which demonstrates their common ancestry.