23.【問(wèn)題背景】如圖1,△ABD,△ACE均為等邊三角形.求證:DC=BE;
【解決問(wèn)題】△ABC為等邊三角形,點(diǎn)D在邊AB上,點(diǎn)E是邊AC上一個(gè)動(dòng)點(diǎn)(不與點(diǎn)A,點(diǎn)C重合),以DE為邊作等邊△DEF.
①如圖2,若點(diǎn)D與點(diǎn)B重合,點(diǎn)G在BA延長(zhǎng)線上,且ED=EG.試探索線段CF,AG,AB之間有何數(shù)量關(guān)系?并證明你的結(jié)論;
②如圖3,若△ABC的邊長(zhǎng)為5,EF=FC.求AD的長(zhǎng).