I get tired of arguing this point, in large part because I can't do it very well without notes and diagrams - I'm not really that smart or that cool. However, it comes up again and again; most recently, it came up when I tried to defend the sanctity of pigeons on the basis of their being dinosaurs (and this being, of course, a good reason for me to feed them my bread crumbs right from the table at a French bistro). My assertion of this point led to a good deal of head shaking and chuckling to the purpose of making me feel stupid. But no! I rested easy in my knowledge that I would soon be home and buried in my books and notes and papers and anatomical drawings, and thus appropriately armed, could write a largely-ignored blog post on the topic.Any kid worth their salt in basic, vague dinosaur knowledge, knows about Archaeopteryx, the feathered, flighted dinosaur. It's long since been accepted that Archaeopteryx is a member of the clade Aviale due to its feathers: all birds have feathers; Archaeopteryx has feathers; Archaeopteryx is a bird. Since Archaeopteryx is clearly a member of Aviale, it's easy to do a cladistic analysis to see the relationship of living birds to dinosaurs, because we only need trace the higher taxanomic relationships of Archaeopteryx.
BTW: Cladistics refers to the use character hierarchies to establish groups with shared derived characters, illustrating the creation of new species from ancestral populations. These groups are called clades, which includes an ancestor and all of its descendants. A monophyletic clade is one that is evolved from a common ancestor - and living birds are in fact a monophyletic group. For some illustration of this crap, look at my handy little diagram (which, in addition to a couple of cladograms, also includes my annotated pigeon skeleton as a bonus).
So... Cladistically, if you follow the various diagnostic characteristics of Archaeopteryx, starting with the Archosauria (which includes crocodiles), all the way to the clade of Aviale (which includes modern birds), it shows that birds must, indeed, be members of the Dinosauria clade. Both birds and Archaeopteryx possess, 1) an antoribital opening on the skull, thus making them both members of the clade Archosauria, 2) a four-toed clawed foot, with symmetry around digit III, and digit I reduced, thus making them members of the clade Ornithodira (although digit I is rotated backwards in living birds, rather than lying alongside digit II), 3) three or more sacral vertebrate, a reorientation of the shoulder, reduction of the fourth finger in the hand, and a semi-perforate acetabulum, thus making making them members of the clade Dinosauria. Dinosauria = dinosaurs! Heyyyy-oooooh!
The conclusion: Archaeopteryx is placed within Aviale as well as Dinosauria, therefore birds must be a subset of Dinosauria. BAM.
