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"To be" and similar verbs are called stative verbs (verbs of state), as opposed to active verbs (verbs of action). Only active verbs can be transitive or intransitive. Transitivity doesn't apply to stative verbs. Also, the predicate is just the part of the sentence that isn't the subject. So after a stative verb is what's called a subject complement, which is often a predicate nominative or a predicate adjective.
This should explain it: