题目

Flying over a desert in an airplane, two scientists looked down with trained eyes at trees and bushes. After an hour's flight one of the scientists wrote in his notebook, Look here for probable metal. Walking across hilly ground, four scientists reported, This ground should be searched for metals. From an airplane over a hilly wasteland a scientist sent back by radio one word Uranium.     None of the scientists had X-ray eyes: they had no magic powers for looking down below the earth's surface. They were merely putting to use one of the newest methods of locating minerals in the ground -- u7．如图，在平行四边形ABCD中，∠ABD=30°，AB=4，BD=5$\sqrt{3}$，将△BCD沿方向平移BD，得到△EFG．（1）连结AE、DF，求证：四边形AEFD为平行四边形．（2）若?AEFD为矩形，求△BCD平移的距离BE．