如圖1,Rt△ABC中,∠ACB=90°,AC=BC,D為CA上一動(dòng)點(diǎn),E為BC延長(zhǎng)線上的動(dòng)點(diǎn),始終保持CE=CD.連接BD和AE,將AE繞A點(diǎn)逆時(shí)針旋轉(zhuǎn)90°到AF,連接DF.
(1)請(qǐng)判斷線段BD和AF的位置關(guān)系并證明;
(2)當(dāng)
時(shí),求∠AEC的度數(shù);
(3)如圖2,連接EF,G為EF中點(diǎn),
,當(dāng)D從點(diǎn)C運(yùn)動(dòng)到點(diǎn)A的過(guò)程中,EF的中點(diǎn)G也隨之運(yùn)動(dòng),請(qǐng)求出點(diǎn)G所經(jīng)過(guò)的路徑長(zhǎng).