来自秦伟的问题
已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
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2020-12-03 02:42
已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
已知:AD平分∠BAC,AC=AB+BD,求证:∠B=2∠C.
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...