已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
问题描述:
已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
答
如图,在AC上截取AE=AB,连接DE,∵AD平分∠BAC,∴∠BAD=∠EAD,在△ABD与△ADE中,∵AE=AB∠BAD=∠EADAD=AD,∴△ABD≌△ADE,∴∠B=∠AED,DE=BD,∵AB+BD=AC=AE+CE,∴DE=CE,∴∠EDC=∠C,∴∠AED=∠C+∠EDC...