According to the conclusion analysis, point G is the intersection of EC and BF, not excuse me.

Solution: (1) because DB=DF? ∴∠DBF=∠F？

Because af ∨ BC ∴∠ CBF = ∠ F.

∴∠DBF=∠CBF？ That is, BF bisection ∠DBC

(3) because of Germany ∨ BC? DE=CD=BC again

∴ quadrilateral BCED is a parallelogram.

∴BD∥CE∴∠EGF=∠DBF

Also ∠DBF=∠CBF

∴∠EGF=∠F

∴EG=EF

(4) Because DF=DB=√(2)DC=√(2)

Germany =DC= 1

∴EG=EF=DF-DE=√(2)- 1

(2) If DI⊥CE is in I, then ∠ FDI = 45,

Because DE=DA? ∠CDE=RT∠？ ∴∠DEC=45

From (1), ∠ f = ∠ DBF = 45/2 = 22.5

∴∠DHG=90-22.5=67.5

Obviously di/de =1√ (2) = √ (2)/2.

EG=√(2)- 1 from (4)

GI =(CE/2)-EG =√(2)/2-(√(2)- 1)= 1-(√(2)/2)

∴gi/ge=[ 1-(√(2)/2)]/(√(2)- 1)=√(2)/2

∴DI/DE=GI/GE

∴GD equally divided

∴∠EDG=45/2=22.5 =∠F

∴GD=GF

∴∠GDH=90-22.5=67.5 =∠DHG

∴GD=GH

∴DG=HG=GF.

(5) Because S△DCE= 1/2? 1? 1= 1/2

S△DGE/S△DEC = GE/CE =(√( 2)- 1)/√(2)

s△DGE/( 1/2)=(√( 2)- 1)/√(2)

∴S△DGE=(2-√(2))/4