19.如圖,已知△ABC的高AE=5,BC=
,∠ABC=45°,F(xiàn)是AE上的點(diǎn),G是點(diǎn)E關(guān)于F的對(duì)稱點(diǎn)
,過(guò)點(diǎn)G作BC的平行線與AB交于H、與AC交于I,連接IF并延長(zhǎng)交BC于J,連接HF并延長(zhǎng)交BC于K.
(1)請(qǐng)你探索并判斷四邊形HIKJ是怎樣的四邊形?并對(duì)你得到的結(jié)論予以證明;
(2)當(dāng)點(diǎn)F在AE上運(yùn)動(dòng)并使點(diǎn)H、I、K、J都在△ABC的三條邊上時(shí),求線段AF長(zhǎng)的取值范圍.