Disclaimer: I don't know your level of knowledge, so I'm making this as simple as possible.....
Here's part of the rear suspension under my '87 (same design as your LT1 car):
The red piece in the center is my BMR torque arm. That is connected to the rear and the transmission.
The light blue part that's off to the left just inboard of the rear tire is one of the rear lower control arms (LCA). There is another one in the same spot on the other side.
Just to the right of the LCA you can see a thin strip of yellow. That is one of my rear shocks. Again, there is one in the same spot on the other side.
The black/rusty u-shaped stamped-steel bar going horizontally across the back (behind the axle) is the panhard bar. That centers the rear axle under the car.
- Justin