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Dear Student,

In a parallelogram opposite angles are equal therefore,
∠∠ABC = ∠∠ADC 
Now, ∠∠ABC + ∠∠EBC = 180              (Linear Pair angles)
∠∠EBC = 180 - ​ ∠∠ABC   ............. (1)

Also, ​∠∠ADC + ∠∠CDF = 180              ​(Linear Pair angles)
∠∠CDF = 180 - ​∠∠ADC   ............... (2)
From (1) and (2) ,
∠∠EBC = ​∠∠CDF      ..............(3)       (Since ​∠∠ABC = ∠∠ADC ) 

Opposites sides of a parallelogram are equal therefore
AB = DC 
but, AB = BE
hence, DC = BE        ............ (4)

Similarly, DF = BC  ............ (5)

In triangle BEC and triangle DCF

BE = DC                      (From (4) )
∠∠EBC = ​∠∠CDF          (From (3) )
BC = DF                      (From (5) )

Therefore the two triangles are similar by SAS (Side Angle Side) test

Regards