Especially if you grew up with “The land before time” it’s easy to imagine a T-Rex frolicking with a Stegosaurus. However, the Stegosaurus existed about 155-150 million years ago while the T-Rex existed about 68-66 million years ago. They would never have met, unless they met on the set of Jurassic Park or something like that.

I normally try to use other sources than Wikipedia, but for well-established things like this it’s a good starting-place to read more. 
https://en.wikipedia.org/wiki/Stegosaurus
https://en.wikipedia.org/wiki/Tyrannosaurus