Final answer:
Mammals and birds share characteristics like endothermy and a dorsal, hollow nerve cord, and both lay amniotic eggs, but they do not share an archosaur common ancestor. Mammals evolved from synapsids, while birds are descended from diapsids within the archosaur branch.
Step-by-step explanation:
The student question pertains to the characteristics shared between mammals and living birds. Three of the options given are common characteristics: endothermy, having a dorsal, hollow nerve cord, and laying an amniotic egg. However, the characteristic that mammals and living birds do not share is 'An archosaur common ancestor'. Mammals and birds did indeed both evolve from amniote ancestors but their direct lineages split early on into separate branches: mammals evolved from synapsids while birds are descended from the archosaur branch of diapsids. Specifically, archosaurs gave rise to reptiles like crocodiles, dinosaurs, and eventually birds, but not mammals.
Mammals are identified by features such as hair or fur, mammary glands, and also share the trait of being endothermic with birds. Both groups utilize a terrestrially adapted egg with protective amniotic membranes, an evolutionary adaptation that distinguished them from amphibians and allowed for greater terrestrial habitation. However, most mammals give birth to live young, with the exception of monotremes like the platypus and echidna that lay eggs.