Final answer:
The Fatimid dynasty is named after Fatima, the daughter of the Prophet Muhammad. The dynasty founders claimed descent from her, establishing their legitimacy as Shia Imams and rulers.
Step-by-step explanation:
The Fatimid dynasty is named after Fatima, the daughter of the Prophet Muhammad. The founder of the Fatimid Caliphate, Abu Muhammad Abdullah, claimed descent through Ali's wife and Muhammad's daughter Fatima. This claim was central to the Fatimid caliphs' legitimacy as they also claimed to be Imams, holding spiritual authority over Muslims. The Fatimids, being part of the Shi'a faction of Islam, believed in the hereditary leadership through Ali and Fatima's lineage, which distinguished their claim to the caliphate from the Sunni Abbasid rule. The Fatimids rose to power in the tenth century and conquered Egypt in 969, founding the city of Cairo as their new capital.