ABCD是平行四边形.用^2表示平方过A作AE垂直BC,过D作DF垂直BC于F.那么,BE=CF,所以EF=BC AC^2=AE^2+(BC-BE)^2 BD^2=DF^2+(BC+CF)^2因为 AE=DF,BE=CF,所以 AC^2+BD^2=2AE^2+2BC^2+2BE^2=2(AE^2+BE^2)+2BC^2=2AB^2+2BC^2...