It is a balancing act to shoot photos of dancers during a live performance. Lighting, stage position, the size of the theater, and the audience are all variables you have to contend with. Wise choices always start with the lens(es) you choose.
My go to lens for these sort of unknown venues - ones where you can guess that you will probably be a fair distance from the subject(s) but not so far as to require a heavy and large super-telephoto - is the Nikon 70-200 f/2.8 - or the older 80-200 f/2.8 The history of these lenses is pretty straight forward... Nikon's professional telephoto zoom lens was originally 80-200mm with a max aperture of f/2.8 until the advent of the VR lenses (Vibration Reduction). The focal length was changed to 70-200mm with a max aperture of f/2.8.
I have both - and depending on the situation I will choose one or the other.
Having a zoom lens allows you to pull out or push in enough to capture close-up action or wider ensemble shots.
This is also helpful if you want to capture photos which display scale - for instance the height a dancer is able to reach during a mid-air split.
Having a fast aperture @ f/2.8 - while being far enough away from the stage to not disturb those around you with the sound of your shutter ( at 11 frames per second my Nikon D4s sounds like a machine gun) - also gives you enough distance from the subject that your depth of field at your point of focus will be a couple of feet. This helps minimize focus errors.
ISO is important - because you want your shutter speed to be 1/1600 second or higher - so you can capture the dance moves in perfect focus with zero motion blur.
With the Nikon D4s - with zero in camera noise reduction selected (because this can take extra processing time and slow down your frame rate) - I don't usually go above 12,000 ISO. Which sounds like a lot - but all of these photos were shot between 6400ISO and 12,000ISO - and using slight noise reduction in PhotoRAW - you can see that there is no loss of detail.
The most important thing to me when shooting live performances is to do everything within my power to NOT cause a distraction or take away from the performance. I choose shooting positions that are away from the audience so the sound of my camera isn't an irritation. Also - it goes without saying - but I feel I should say it anyway - you NEVER use a speedlight (flash) - in these situations. The flash of the speedlight can be dangerous to the performers for it can momentarily blind them. Most every theater - auditorium shoot I've ever done has had ample light - so long as you bring the right lens(es) for the job.