Final answer:
The transitional section between the dome and the rectangular base in Hagia Sophia is a pendentive, which supports the dome and allows for a circular dome to be placed over a square room.
Step-by-step explanation:
The transitional section between the dome and the rectangular base in Hagia Sophia is known as a pendentive. A pendentive is an architectural device used to support a circular dome over a rectangular room or space. It allows for the placement of a round dome over a square room by transitioning the weight and structure from a circular base to the flat corners of the square below. The acknowledgment of pendentives is crucial in the understanding of Byzantine architecture, particularly in structures like Hagia Sophia, which was constructed under the direction of Emperor Justinian with the intent of making it the grandest church. As such, it featured a central dome as the principal emphasis, supported by massive architectural innovations including the use of pendentives.