Final answer:
During Trajan's reign, the Roman Empire expanded to its greatest geographical extent, which validates option E as the correct answer.
Step-by-step explanation:
The reign of Emperor Trajan was notable for multiple achievements, among which was the significant territorial expansion of the Roman Empire. Under his leadership, the empire reached its greatest geographical extent in 117 CE, encompassing regions from most of England across to parts of the Middle East and North Africa, including modern-day Romania and Morocco, and extending to the borders of the Parthian Empire. Trajan was lauded not just for his military conquests, such as those in Dacia (now Romania), but also for his administrative excellence and efforts to maintain stability within the empire, working closely with the Senate. The option that best encapsulates Trajan's reign would be E) the Roman Empire reaching its greatest geographical extent.