25.如圖,在Rt△ABC中,AB=AC,∠BAC=90°,F(xiàn)為直線AB上一點(diǎn),連接FC,作BD⊥FC于點(diǎn)D,連接AD,過點(diǎn)A作AE⊥AD交BD于點(diǎn)E.
(1)如圖1,求證:AD=AE;
(2)如圖2,若點(diǎn)H是BD中點(diǎn),連接AH、CE,求證:CE=2AH;
(3)如圖3,當(dāng)點(diǎn)F運(yùn)動到線段AB上且不與A、B重合時,連接CE,過點(diǎn)A作AH⊥CE交BD于點(diǎn)H,H為BD中點(diǎn),猜想CE與AH之間的數(shù)量關(guān)系并證明.