(2008? Yantai) As shown in the figure, the side length of rhombic ABCD is 2, BD=2, E and F are two moving points on the sides of AD and CD respectively, AE+CF = 2.
( 1)AE+CF=2=CD=DF+CF
∴AE=DF
AB=BD
∠A=∠BDF=60
∴△BDE is equal to △ △BCF.
(2) BE=BF from (1)
And ∠ EBF = ∠ EBD+∠ DBF = ∠ EBD+∠ Abe = ∠ Abd = 60.