Given the parallelogram ABCD, make the equilateral triangle ade and equilateral triangle BCF outward with AD and BC, connect be and DF, and find be = DF

Given the parallelogram ABCD, make the equilateral triangle ade and equilateral triangle BCF outward with AD and BC, connect be and DF, and find be = DF

prove:
A quadrilateral ABCD is a parallelogram
∴AB=CD,AD=BC,∠BAD=∠BCD
∵ △ ade and △ BCF are equilateral triangles
∴AE=AD=BC=CF,∠EAD=∠BCF=60°
∴∠BAE=∠DCF
∴△BAE≌△DCF
∴BE=DF