Uh, yeh, they did. They were known as "badassaurs". The Gigantasaur or whatever was an Aregentine monster that lived during the Triassic. T-Rex lived during the Cretaceous. As quoted from http://www.dinotreker.com/cretaceous.html
"The Cretaceous Period 144 to 65 million years ago saw even more diverse and unusual dinosaurs. Some of these dinosaurs would include: The Ankylosaurus with its club-like tail and the Sauropelta with its armor plating and spikes. Dinosaurs with huge sails on their backs such as Spinosaurus and the more recently discovered Suchomimus were included among these unusual dinosaurs. Crested dinosaurs, such as Parasaurolophus were said to use their hollow crest for communication, creating low tone vibrations similar to that of Whales and Elephants. The horned dinosaurs such as the Triceratops, Chasmosaurus and Torosaurus, which had bird-like beaks also lived during this period. The theropods with slashing claws on their feet, which included Deinonychus, Velociraptor and the larger Utahraptor, also stalked the Earth during this time. The very large carnivorous theropods, such as the Tarbosaurus, Albertosaurus and the infamous Tyrannosaurus rex roamed the plains and forests in the hunt for food during The Cretaceous Period."