如圖,在正方形ABCD中,E,F(xiàn)分別是AD,CD上的點(diǎn),且AE=CF,M,N分別是EF,EB的中點(diǎn),延長AN交BF于點(diǎn)K.
(1)①小明通過畫圖探究得到以下數(shù)據(jù),根據(jù)題意,將表格補(bǔ)充完整.
∠FBC |
10° |
20° |
40° |
∠EBF |
70° |
50° 50°
|
10° 10°
|
∠BNK |
20° |
40° 40°
|
80° 80°
|
②寫出∠EBF與∠BNK的數(shù)量關(guān)系,并給出證明.
(2)當(dāng)四邊形MNKF中有一條邊是NK的2倍時(shí),求cos∠EBF的值.
(3)直線MN分別交AB,CD于點(diǎn)P,Q,延長EF交射線BC于點(diǎn)G,當(dāng)點(diǎn)G關(guān)于直線BF的對稱點(diǎn)落在直線MN上時(shí),直接寫出
的值.