Final answer:
A peg-in-socket fibrous joint is known as a gomphosis, distinguished by its immobility and the presence of periodontal ligaments.
Step-by-step explanation:
A fibrous joint that is a peg-in-socket shape is called a gomphosis joint. The periodontal ligament connects the root of a tooth to its bony socket in the jaw, and this union is classified as a synarthrosis due to its immobility. Other types of fibrous joints include sutures, found between skull bones, and syndesmoses, which allow for more movement between bones connected by connective tissue.