Stageplay in gym
 

I will be shooting a school stageplay performed in a gym. The only mics will be two mics hung above the stage going to the soundboard. My plan is to connect one input of my PD170 to the soundboard, set up an AT 873R in front of the center of the stage and connect that to the other input on the cam with the thought that the 873R will obtain clearly understandable dialogue from the actors moving about the stage.
I suppose it would be better to set up two hypercardiods at the front of the stage and run them into a mixer, better yet to mic the actors with lavs, but resources for this particular shoot are limited and only the one mic is available, aside from the two above the stage.
My question is, is the 873R a good choice for this application? Is there a better low-cost solution?

There's one other mic in that price range that would be better, the AT3031.
The AT873r is very good at picking up clean dialogue. It does have higher self-noise and a tighter pattern. If the actors are quiet or they move more than 45 degrees away from the mic, you will start to have difficulties. But it's still alot better in that situation than many other mics.
If the two mics hanging over the stage are a spaced pair and they are being mixed together equally and then left alone, this will sound pretty bad.
If they are hung close together in a coincident stereo pair, then they will sound a little better. For work on stage that's ending up as a mono signal, an odd number of mics like 1 or 3 works much better. And having someone actively mix them sounds even better.

Jay,
Thanks. Sounds like I would be better off not bothering with the hanging mics and connecting to just the 873R or 3031.
Between the two AT mics, does one provide wider pickup as the actors move across the stage? This is an issue for this shoot, limited to a single mic as it is.

The 3031 has a wider pickup pattern than the 873r. Of course as the actors move to the sides of the stage they not only change angle to the mic but they get further away too, so a wider pickup isn't a perfect solution to this change in volume but it helps.
You'll have to compromise on how close you put the mic to the stage to try and equalize the distances involved. And making sure nobody trips over your mic, stand and cable is even more important unfortunately. Generally 2 to 5 feet from the front edge is acceptable. I aim upward slightly so that you're pointing at head level of someone who is about 15 to 20 feet from the edge of the stage.
There are other factors to consider with using the house mics and a feed from that system. Is it a lot of trouble to run balanced cable from this system? Does this system even sound good? Does this connection cause a ground-loop hum? Does this system give you better coverage during some parts of the play than your single front-mic? Are you better served using your mic switched to both recording channels with one set slightly lower as a safety against loud passages from the actors?

Thanks, Jay. You've been very helpful.