3 bright lights in very large triangle formation. All moving together as one, heading North. Then they started to separate.

I was taking my dog for his nightly walk when I saw a plane. The plane still had its landing lights on, and looked kind of cool in the night sky. While watching it I saw what I originally thought was stars in a perfect triangle formation. The plane was starting to go behind some trees so I turned my attention back to what I thought was stars. As I was watching I noticed that they were actually moving in a northern direction. The most northern one then seemed to speed up and split from the other two. It quickly disappeared. As I focused on the other two, the one towards the east shot off in that direction, and the final one appeared to fade out. They appeared to be much higher than the plane, and spread out a great distance. While it's likely just a strange coincidence, I had turned off my headlamp to watch the plane. After the plane and objects left I went to turn my headlamp back on and the batteries were dead.