25.如圖1,折疊矩形紙片ABCD,具體操作:①點(diǎn)E為AD邊上一點(diǎn)(不與點(diǎn)A,D重合),把△ABE沿BE所在的直線折疊,A點(diǎn)的對(duì)稱點(diǎn)為F點(diǎn);②過點(diǎn)E對(duì)折∠DEF,折痕EG所在的直線交DC于點(diǎn)G,D點(diǎn)的對(duì)稱點(diǎn)為H點(diǎn).
(1)求證:△ABE∽△DEG.
(2)若AB=3,BC=5,
①點(diǎn)E在移動(dòng)的過程中,求DG的最大值;
②如圖2,若點(diǎn)C恰在直線EF上,連接DH,求線段DH的長.