Because: △ABE folds along BE to get △GBE.

So AB=BG, AE = eg.

Because AE=ED

So EG=ED

So angel ·EGD = angel ·EDG

However, angle EGD+ angle FGD= angle EDG+ angle FDG=90 degrees.

So angle FGD= angle FDG

So GF=DF

(2) Because GF=DF, BG=AB=DC=2DF.

So BF=BG+GF=BG+DF=3DF.

Because DC=2DF, DF = CF

So BC 2 = BF 2-FC 2 = (3dF) 2-DF 2 = 8dF 2.

So BC=2 times the root number 2DF.

So AD/AB=BC/AB=2 times the root number 2.

(3) Ask and answer (2) Prove in the same way. Self-proof method 2.