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Yes, the Allosaurus was a large theropod, a carnivorous dinosaur.
The general consensus is that they evolved from a group of small theropod dinosaurs.
Troodon
Yes.
Maniraptora is the name of a group of theropod dinosaurs.
Archaeopteryx, Velociraptor, Troodon andmodern day birds are examples maniraptorian theropod dinosaurs.
a tyranosaurus is a theropod