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if DF + BE = AE then ABCD is square, <DAF=<FAE (2002 Romania District VII P4)

Source:

May 23, 2020
equal anglesgeometrysquarerectangle

Problem Statement

Given the rectangle ABCDABCD. The points E,FE ,F lie on the segments (BC),(DC)(BC) , (DC) respectively, such that ∠DAF=∠FAE\angle DAF = \angle FAE. Proce that if DF+BE=AEDF + BE = AE then ABCDABCD is square.
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