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The eighth grade math teacher guides the students.
Syndrome: the intersection of FD and AC is g.

∫AE divides ∠BAC, ∠ BAC = 90.

∴∠BAE=∠CAE=45

∵FD⊥BC

∴∠CDG=90

∠∠CGD = 180-∠CDG-∠C

∠B= 180 -∠BAC-∠C

∴∠B=∠CGD

∴∠AFG=∠CGD-∠CAE=∠B-45

∠∠CAD =∠C,∠B+∠C=90,∠CAD+∠BAD=90

∴∠B=∠BAD

∠∠BAD =∠BAE+∠DAE = 45+∠DAE

∴∠DAE=∠B-45

∴∠DAE=∠AFG

∴AD=DF