, because AD is the center line of triangle, BD=CD, so △ bgd △ ADC is AC//BG.

∠BGD=∠DAC, AC=BGAC=BG because AE=EF, that is, △AEF is an isosceles triangle.

So ∠EAD=∠AFE=∠BFD=∠BGD, that is, △FBG is an isosceles triangle.

BG=BF AC=BF because AC=BG.