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.