25.如圖1,四邊形ABCD為正方形,點(diǎn)E為AD上的定點(diǎn),點(diǎn)F是射線BE上的動(dòng)點(diǎn),連接AF.將點(diǎn)F繞點(diǎn)A逆時(shí)針旋轉(zhuǎn)90°得到點(diǎn)H,連接AH,過(guò)點(diǎn)F,H分別作AF和AH的垂線交于點(diǎn)G,射線DH與射線BE交于點(diǎn)P.
(1)求證:四邊形AFGH為正方形;
(2)點(diǎn)F在運(yùn)動(dòng)過(guò)程中,判斷點(diǎn)P的位置是否發(fā)生變化?并說(shuō)明理由;
(3)連接CG,PG,AP,探究線段AB,AP,CG,PG的數(shù)量關(guān)系,并證明.