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Xiangyang zhongkao mathematics
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.