Final answer:
The Western Roman Empire and the Roman Catholic Church both were based in Rome. While the empire fell in 476 CE, the Church continued to thrive and preserve Roman culture. Option D is the correct answer.
Step-by-step explanation:
The common feature shared by the Western Roman Empire and the Roman Catholic Church is that both were based in Rome. The Western Roman Empire was the western part of the Roman Empire that, after much decline, ultimately fell in 476 CE. In contrast, the Roman Catholic Church, centered in Rome, managed to survive the fall of the empire and evolved to unite Western Europe culturally and spiritually. It played a crucial role in preserving many aspects of Roman culture, including the use of Latin, which remained the language of the Church until 1965.