1.如圖,在長(zhǎng)方形ABCD中,AB=12,BC=16,點(diǎn)E是BC邊上一點(diǎn),連接AE,將∠B沿直線AE折疊,使點(diǎn)B落在點(diǎn)B′處.
(1)直接寫(xiě)出AC的長(zhǎng)度;
(2)如圖1,當(dāng)點(diǎn)E不與點(diǎn)C重合,且點(diǎn)B′在對(duì)角線AC上時(shí),求CE的長(zhǎng);
(3)如圖2,當(dāng)點(diǎn)E與點(diǎn)C重合時(shí),CB′與AD交于點(diǎn)F,求證:FA=FC.