Final answer:
The quadrate lobe is adjacent to the gallbladder. It is situated in the right lobe of the liver, which has several connections to peritoneal folds and vessels that facilitate its complex functions.
Step-by-step explanation:
The quadrate lobe of the liver is adjacent to the gallbladder. This is seen in the anatomy of the liver which includes a large right lobe and a smaller left lobe. Within the right lobe, the quadrate lobe is situated inferiorly and is next to the gallbladder, which stores and concentrates bile produced by the liver. The liver's connection to other structures, including the gallbladder and blood vessels such as the hepatic portal vein and hepatic artery, is facilitated by peritoneal folds or ligaments, such as the lesser omentum.