已知:如图,AD=AE,BD=CE,∠ADB=∠AEC,求证:△ABE≌△ACD.

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已知:如图,AD=AE,BD=CE,∠ADB=∠AEC,求证:△ABE≌△ACD.

已知:如图,AD=AE,BD=CE,∠ADB=∠AEC,求证:△ABE≌△ACD.
已知:如图,AD=AE,BD=CE,∠ADB=∠AEC,求证:△ABE≌△ACD.

已知:如图,AD=AE,BD=CE,∠ADB=∠AEC,求证:△ABE≌△ACD.
∵AD=AE,BD=CE,∠ADB=∠AEC
∴△ABD≌△ACE
∴AB=AC
∵BE=BD+DE
CD=CE+DE
∴CD=BE
∴:△ABE≌△ACD

△ADB≌△AEC
AB=AC,∠B=∠C
∴BE=CD
∴△ABE≌△ACD