What is the Eastern Catholic rite?

Answer 1

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Catholic AnswerThere are several Rites in the Catholic Church, of which the Latin Rite (sometimes called the Roman Rite) is the principle one in the West. There are many different Rites in the Eastern Church. When the Schism of the East occurred in the eleventh century, most of the Eastern Rites split in two, which half remaining with the Catholic Church, they are referred to as "Uniate Rites" and half forming a new Orthodox Church. Thus there is a Greek Uniate Rite, and a Greek Orthodox Church, etc.

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from The Catechism of the Catholic Church, second edition, English translation 1994

1203 The liturgical traditions or rites presently in use in the Church are the Latin (principally the Roman rite, but also the rites of certain local churches, such as the Ambrosian rite, or those of certain religious orders) and the Byzantine, Alexandrian, or Coptic, Syriac, Armenian, Maronite, and Chaldean rites. In "faithful obedience to tradition, the sacred Council declares that Holy Mother Church holds all lawfully recognized rites to be of equal right and dignity, and that she wishes to preserve them in the future and to foster them in every way." (Sacrosanctum concilium 4)