Because AB =AD, ∠ABD=∠ADB.

Because ∠ADB = ∠CDE, ∠CFE=∠ADB

Because AD is the bisector of ∠BAC, ∠BAD=∠DAC.

So △ABD is similar to △AFC.

So ∠ABD= ∠ACF

That is ∠AFC=∠ACF

So AB = AC

That is, AD+2DE = AC.

2) extend DE to point f to make AE =EF and connect CF, then ∠CFE = ∠CAE. CF=AC。

Because AB =AD, ∠ABD=∠ADB.

Because ∠DAG = ∠CAE, ∠CFE=∠DAG.

Because AD is the bisector of ∠BAC, ∠BAD=∠DAG.

So ∠CFE = ∠BAD.

So △ABD is similar to △ △CDF.

Then ∠FCD=∠ABD

So ∠FCD= ∠FDC

That is, CF=FD=AD+2AE=AC.

3)

AD+AE=2AC