What's the best way to transition JavaScript framework?

We're currently using AngularJS for our front-end, API-driven, web app. We're building a brand new section in our application and we're thinking of doing it in React, but keeping the UX consistent and running both app simultaneous. At least that's the hope.

The idea is to not continue building out new functionalities on an EOL framework, but also not rewriting the entire app in one shot since that's just not possible at this time.

It seems that this is a common pattern among many large applications because you can tell when you go from "new" facebook to "old" facebook, or paypal, etc...

If anyone has experience with maintaining two separate JS application, what is your advice? Is this a mistake?