23.(1)【探究發(fā)現(xiàn)】如圖①,已知矩形ABCD的對(duì)角線AC的垂直平分線與邊AD,BC分別交于點(diǎn)E,F(xiàn).求證:四邊形AFCE是菱形;
(2)【類比應(yīng)用】如圖②,直線EF分別交矩形ABCD的邊AD,BC于點(diǎn)E,F(xiàn),將矩形ABCD沿EF翻折,使點(diǎn)C的對(duì)稱點(diǎn)與點(diǎn)A重合,點(diǎn)D的對(duì)稱點(diǎn)為D',若AB=3,BC=4,求四邊形ABFE的周長(zhǎng);
(3)【拓展延伸】如圖③,直線EF分別交平行四邊形ABCD的邊AD,BC于點(diǎn)E,F(xiàn),將平行四邊形ABCD沿EF翻折,使點(diǎn)C的對(duì)稱點(diǎn)與點(diǎn)A重合,點(diǎn)D的對(duì)稱點(diǎn)為D',若
,BC=4,∠C=45°,求EF的長(zhǎng).