23.已知△ABC中,∠B=60°,點(diǎn)D是AB邊上的動(dòng)點(diǎn),過點(diǎn)D作DE∥BC交AC于點(diǎn)E,將△ADE沿DE折疊,點(diǎn)A對(duì)應(yīng)點(diǎn)為F點(diǎn).
(1)如圖1,當(dāng)點(diǎn)F恰好落在BC邊上,求證:△BDF是等邊三角形;
(2)如圖2,當(dāng)點(diǎn)F恰好落在△ABC內(nèi),且DF的延長線恰好經(jīng)過點(diǎn)C,CF=EF,求∠A的大?。?br />(3)如圖3,當(dāng)點(diǎn)F恰好落在△ABC外,DF交BC于點(diǎn)G,連接BF,若BF⊥AB,AB=9,求BG
的長.