如图,AB=AC,AD=AE,AB,DC相交于点M,AC,BE相交于点N,∠DAB=∠EAC.求证:△ADM≌△AEN.
问题描述:
如图,AB=AC,AD=AE,AB,DC相交于点M,AC,BE相交于点N,∠DAB=∠EAC.求证:△ADM≌△AEN.
答
证明:∵AB=AC,AD=AE,∠DAB=∠EAC,
∴∠DAC=∠AEB,
∴△ACD≌△ABE,
∴∠D=∠E,
又AD=AE,∠DAB=∠EAC,
∴△ADM≌△AEN.