They formally split the Christian Church apart They created two completely separate churches.
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They were not. Both the Orthodox and Roman Catholics accept the decision of the Seventh Ecumenical Council which declared that the veneration of icons is essential in the Christian Church. The split (or schism) was due to other causes, such as Papal claims of supremacy, and the change to the Creed.
Byzantium, renamed Constantinople (now Istanbul) became capital of the eastern Roman Empire when the empire was split into two.
The Roman Empire split into two pieces, the Western Empire whose capitol was still in Rome, and the Eastern with its capitol in Constantinople, modern Istanbul.
The Fourth Crusade in 1204 AD resulted in the sack of the Eastern Orthodox City of Constantinople by the Roman Catholic crusaders. This increased tensions and caused enormous damage in relations between East and West and solidified the split that happened 150 years earlier in 1054 AD (the Eastern Schism).
Because the Muslims invaded Constantinople so they took over. Your welcome hope that this was helpful.
The iconoclasm did not lead to any split. It led to a compromise in which statues were not to be used and icons were to be painted in the Byzantine style. The answer "The Great Schism of 1054" is often given, even though that happened due to a power feud between two bishops who got so angry they excommunicated each other.
They were mostly Christian, and after 1054, split from the catholic, or universal church, and are usually referred to as "Greek Orthodox."
No, Constantinople was the capital of the Byzantine Empire. The Byzantine Empire was the Eastern split of the Roman Empire and later ruled from Rome through Southeastern Europe and Asia Minor, down to Egypt and across North Africa.