Analysis: ∫∠ADB is the inner angle of Rt△ABD and also the inner angle of Rt△ADF, so ∠CDE should also be in a right triangle, which can be associated as an auxiliary line. Point C is that CG⊥AC intersects with AE extension line in G, and Rt△ABD≌Rt△CAG can be obtained from conditions.

It is proved that the passing point C is the CG⊥AC and AE extension line at G.

∵BA⊥AC,CG⊥AC

∴CG‖AB

∴∠ABC=∠BCG (two straight lines are parallel and the internal dislocation angles are equal)

∫∠bad = 90 ,af⊥bd

∴∠ABD=∠CAG (complementary angles of the same angle are equal)

In Rt△ABD and Rt△CAG.

∴∠ABD=∠CAG

AB=CA

∠ bad =∠ACG

∴Rt△ABD≌Rt△CAG(ASA)

∴AD=CG (the corresponding sides of congruent triangles are equal)

∠ADB=∠CGA (the corresponding angles of congruent triangles are equal).

AB = AC

∴∠ABC =∞∠ACB (equilateral and equiangular)

∴∠ACB=∠BCG (equivalent substitution)

∫AD = DC，AD=CG

∴CD=CG (equivalent substitution)

At △DCE and △GCE,

CD=CG

∠BCE=∠GCE

CE=CE

∴△CDE≌△CGE(SAS)

∴∠CDE=∠CGE (the corresponding angles of congruent triangles are equal).

∴∠ADB=∠CDE (equivalent substitution)