Dinosauria is defined as:
The most recent common ancestor of Triceratops horridus and Passer domesticus, and all its descendants.
Fun fact! Before birds were confirmed to be dinosaurs, Passer was replaced by Allosaurus!
This, of course, assumes that Ornithischia + Saurischia = monophyletic clade. I'm still iffy on that proposal, for reasons I've gone into before. Still, if you're ever on Jeopardy, and that's the answer, you can buzz in and say "Dinosauria!"
Thanks to Jerry for pointing out that sparrows are not the same as pigeons. :-)