No, the T. Rex was not from the Triassic period. It lived much later, during the Late Cretaceous period, around 68 to 66 million years ago.
The Triassic period occurred much earlier, spanning from about 252 to 201 million years ago. During the Triassic, the first dinosaurs were just beginning to evolve, and the dominant reptiles were different from what we recognize as dinosaurs today.
In summary, T. Rex is actually a member of the theropod dinosaurs and represents a group that thrived during the Late Cretaceous, well after the Triassic period had ended.