Final answer:
Dinosaurs first appeared in the Triassic Period, but became dominant in the Mesozoic Era, particularly after the mass extinction at the end of the Triassic. The Jurassic and Cretaceous periods represented the peak of dinosaur evolution and dominance. Their reign ended with the mass extinction at the end of the Cretaceous Period.
Step-by-step explanation:
The first dinosaurs are known from the Triassic Period, but don't dominate the planet until the Mesozoic Era. During the Triassic Period, which spanned from 245 to 200 million years ago, these creatures branched off from other reptiles and colonized various environments including land, air, and water. Although dinosaurs existed during this time, other species such as huge seed ferns and conifers were more dominant in the forests.
It was not until the Jurassic Period, following a mass extinction event that ended the Triassic, that dinosaurs began to truly flourish. This era, particularly the Jurassic and Cretaceous periods, represented the golden age of dinosaurs, wherein they reached their peak in size and distribution. The end of the Cretaceous Period, and thus the end of the dinosaur dominance, was marked by another mass extinction event around 65 million years ago.