Analysis: The congruence of △AEB and △ADC can be obtained according to the nature of rotation, and ∠EAB=∠CAD, ∠EBA=∠C can be obtained according to the equivalence of congruent triangles corresponding angles, and then ∠ EAB = ∠ EBA = can be obtained by combining the nature of isosceles triangle.

It is proved that rotating △ △ADC can get △△AEB.

∴△AEB≌△ADC，

∴∠EAB=∠CAD,∠EBA=∠C，

∵AB=AC,AD⊥BC，

∴∠BAD=∠CAD,∠ABC=∠C，

∴∠EAB=∠DAB，

∠EBA=∠DBA，

∠∠EBM =∠DBN，

∴∠MBA=∠NBA，

AB = AB，

∴△AMB≌△ANB(ASA)，

∴AM=AN.