Connecting DE, AD, DF

AB = AC, and D is the midpoint of BC.

∴AD⊥BC (three in one)

∠∠A = 90°

∴AD=DC (the center line of the hypotenuse is half of the hypotenuse)

∴∠EAD=∠FCD=45

AE = CF

AD=CD

∴△AED≌△CFD(SAS)

∴DE=DF

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