Final answer:
The Great Schism was a result of disagreements over religious practices and traditions between the eastern and western Christian churches, exacerbated by linguistic and cultural differences, and contrasting views on leadership within the church.
Step-by-step explanation:
The differences between the eastern and western Christian churches in the eleventh century that led to the Great Schism primarily involve disagreements over religious practices and traditions (option a), reflecting deep-seated theological, political, and cultural divides. The eastern (Eastern Orthodox) and western (Catholic) branches of Christianity had been growing apart due to various factors, including linguistic and cultural differences, disagreements over the use of images in worship, and differing views on papal supremacy versus a more collegial structure of ecclesiastical authority.
In 1054, after a series of escalating disputes, representatives of the pope excommunicated the patriarch of Constantinople, who then issued his own excommunication in retaliation. These mutual excommunications underscored the rift, with the eastern church using Greek and allowing married priests, and the western church using Latin and insisting on clerical celibacy. In the subsequent centuries, each church developed its own hierarchical structures and distinct theological and liturgical traditions, solidifying the division that persists to this day.