It is known that ad is the bisector of the outer angle EAC of △ ABC, and ad ‖ BC, then the edge of △ ABC must satisfy______ ．

∵ ad ‖ BC, ∵ ead = ∵ B, ∵ DAC = ∵ C, ∵ ad is the bisector of ∵ EAC, ∵ DAE = ∵ DAC, ∵ B = ∵ C, ∵ AB = AC, that is, the edge of △ ABC must satisfy the condition AB = AC, so the answer is: AB = AC

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