如圖,在△ABC中,AB=AC,D、E分別在BC、AC邊上,且∠1=∠B,AD=DE,求證:△ADB≌△DEC.

如圖,在△ABC中,AB=AC,D、E分別在BC、AC邊上,且∠1=∠B,AD=DE,求證:△ADB≌△DEC.

證明:∵∠B+∠BAD=∠1+∠EDC,又∵∠B=∠1,∴∠BAD=∠EDC.又AB=AC,∴∠B=∠C.又AD=DE,∴ADB≌△DEC.