What are the Performing Arts?
In general an art is the ability to create something. When it comes to performing arts we are talking about the creations where the performer is part of the work. By their nature the performing arts are ephemeral, i.e. that do not last over time rather than one who takes his execution. Music, dance, theatre, poetry (or Declamation in reality) and any performance that has to be put into scene is considered to be an art of this kind.
The oldest should be music and dance as the cave paintings show it. Then was born as an extension of the dance theatre. Apparently it is in Africa where is born as a representation of their everyday and religious activities, then in Egypt, depictions of dramatic life of Osiris are made and the Greeks are the first to create sites for such representations. The Romans expanded throughout the world known that taste for representations are real or fictitious, using masks or not. In the East there are many forms of theatre, dance and other arts with more or less similar to those of West structures.
In America, we can say that the great civilizations exploited all the performing arts. Currently there is a large group of performing arts struggling to emerge, for example says that cinematography is a way to endure the theater but taking into account the animation techniques as part of the cinematic arts this claim falls under its own weight. Animated or not is a performing arts because it has all the relevant resources, in my humble opinion, also requires a framework as it is the same movie or TV where represented and such representation is as ephemeral as any other work.
They can also be seen as performing arts video games where the viewer not only is watching the work, also participates primarily in role-playing games, as it is the case with many of the circus acts which calls the collaboration of people from the public or the "Dungeons and dragons". I guess I'm much extending the term of performing arts, but the interesting question is why restrict it? My answer would be that it should be extended to cover these new forms of art.