Do the Golgi apparatus and endoplasmic reticulum work together?

Yes, the Golgi apparatus and endoplasmic reticulum work together.

The Golgi apparatus or Golgi complex is located close to the rough endoplasmic reticulum (rough ER) allowing molecules to be easily transported between the two organelles.

Post translational modifications of the proteins occur inside the rough ER. The mature proteins are transported to the Golgi apparatus where they are sorted and packed into sealed droplets called vesicles to be transported to their eventual destination. Depending on the type of protein inside the vesicle, they may be dispatched within the cell to organelles called lysosomes, transported to the plasma membrane of the cell or secreted outside the cell into the extracellular environment.