如图,点D,E在△ABC的边BC上,AB=AC,AD=AE,求证BD=CE http://hiphotos.baidu.com/zhidao/pic/item/aec37931http://hiphotos.baidu.com/zhidao/pic/item/aec379317a1e2034ebc4af1d.jpg

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如图,点D,E在△ABC的边BC上,AB=AC,AD=AE,求证BD=CE http://hiphotos.baidu.com/zhidao/pic/item/aec37931http://hiphotos.baidu.com/zhidao/pic/item/aec379317a1e2034ebc4af1d.jpg

如图,点D,E在△ABC的边BC上,AB=AC,AD=AE,求证BD=CE http://hiphotos.baidu.com/zhidao/pic/item/aec37931http://hiphotos.baidu.com/zhidao/pic/item/aec379317a1e2034ebc4af1d.jpg
如图,点D,E在△ABC的边BC上,AB=AC,AD=AE,求证BD=CE http://hiphotos.baidu.com/zhidao/pic/item/aec37931
http://hiphotos.baidu.com/zhidao/pic/item/aec379317a1e2034ebc4af1d.jpg

如图,点D,E在△ABC的边BC上,AB=AC,AD=AE,求证BD=CE http://hiphotos.baidu.com/zhidao/pic/item/aec37931http://hiphotos.baidu.com/zhidao/pic/item/aec379317a1e2034ebc4af1d.jpg
证明:如图,在△ABC中,已知AB=AC
          ∴∠B=∠C.
         又∵AD=AE
         ∴∠ADE=∠AED, ∴∠ADB=∠AEC.
        在△ADB与△AEC中,∵AB=AC,∠B=∠C,∠ADB=∠AEC.
        根据全等三角形定理得:△ADB≌ △AEC
       ∴BD=CE

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