∵AD=BC, AC=BD, AB=AB (a triangle with three equal sides is congruent triangles).

∴△ABC≌△ABD

∴∠DAB=∠ABC,∠ABD=∠CAB

∠∠CAD =∠DAB-∠CAB，∠DBC=∠ABC-∠ABD

∴∠CAD=∠DBC

2、c

∠∠BAE =∠DAC，∠BAC=∠BAE+∠EAC，∠EAD=∠EAC+∠DAC

∴∠BAC=∠EAD

AB = AD，∠ B = ∠ D。

∴△ABC≌△AED (two corners of a triangle and their corresponding clamping edges coincide)

∴AE=AC

3. At △ACB and △DFE,

∫AB∨DE，BC∨EF

∴∠A=∠EDF, ∠ ACB =∠ DFE (two straight lines are parallel and have the same angle).

AD = CF，AC=AD+DC，DF=DC+CF

∴AC=DF

∴△ACB≌△DFE (coincidence of two corners of a triangle and their clamping edges)

∴AB=DE

4. Connect AC power

In △ACD and △ABC,

AB = AD, DC=CB, ipsilateral AC

∴△ACD≌△ABC (a triangle with three equal sides is congruent triangles)

∴∠B=∠D