如图,在菱形ABCD中,AE⊥BC,垂足为E,AF⊥CD,垂足为F,且BE=EC,CF=DF

连接AC
∵四边形ABCD是菱形
∴BC=DC=AB=AD,∠D=∠B,∠BAD=∠BCD
又∵BE=CE,CF=DF
∴E是BC的中点,F是DC的中点
∴DF=CF=CE=EB
又∵AE⊥BC,AF⊥DC
∴∠AFD=∠AFC=∠AEB=∠AEC=90°
∴△AFD≌△AFC≌△AEB≌△AEC
∴∠ADF=∠ACF=∠ABE=∠ACE
又∵∠B+∠DCB=180°
∴3∠B=180°
∠B=60°
∴∠DCB=120°
∴∠EAF=60°