In retracing steps, the only thing I will add is that when I originally plugged the HDMI cable from the Apple TV box to the receiver linked to the TV and sound system, I did not log in to Apple TV. It was available on the box, of course, but I didn't log in since I was able to stream Apple TV shows from the iPad or iMac through that input to the TV by mirroring So at that point, I was able to show my iPhoto slide shows via the same mirroring. But, I found streaming was not the most convenient way to watch TV so I went ahead and logged in on the connected Apple box to TV*. After that, my TV disappeared from mirroring on my other devices, and, even after I disconnected the box, nothing changed: no mirroring.
As a side point, the Apple TV box seems to have access to all my iTunes library, but it only has a partial collection of my iPhotos, including none of my Photo Albums (and it is very slow at pulling up even this limited collection of photos). The photo options on the iMac and on the iPad are faster and much more extensive; thus, my interest in being able to mirror.
I appreciate the help. Thank you.