已知,BD,CE分别平分∠ABC,∠ACB.AM⊥CE于M.AN⊥BD于N 求证:MN=1/2(AB+AC-AB)视频http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=fc1feb7e3887e9504242fb6a20087f7b/1e30e924b899a9010617bf8b1f950a7b0208f569.jpg
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 21:04:41
![已知,BD,CE分别平分∠ABC,∠ACB.AM⊥CE于M.AN⊥BD于N 求证:MN=1/2(AB+AC-AB)视频http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=fc1feb7e3887e9504242fb6a20087f7b/1e30e924b899a9010617bf8b1f950a7b0208f569.jpg](/uploads/image/z/8803600-16-0.jpg?t=%E5%B7%B2%E7%9F%A5%2CBD%2CCE%E5%88%86%E5%88%AB%E5%B9%B3%E5%88%86%E2%88%A0ABC%2C%E2%88%A0ACB.AM%E2%8A%A5CE%E4%BA%8EM.AN%E2%8A%A5BD%E4%BA%8EN+%E6%B1%82%E8%AF%81%3AMN%3D1%2F2%28AB%2BAC-AB%29%E8%A7%86%E9%A2%91http%3A%2F%2Fc.hiphotos.baidu.com%2Fzhidao%2Fwh%253D600%252C800%2Fsign%3Dfc1feb7e3887e9504242fb6a20087f7b%2F1e30e924b899a9010617bf8b1f950a7b0208f569.jpg)
已知,BD,CE分别平分∠ABC,∠ACB.AM⊥CE于M.AN⊥BD于N 求证:MN=1/2(AB+AC-AB)视频http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=fc1feb7e3887e9504242fb6a20087f7b/1e30e924b899a9010617bf8b1f950a7b0208f569.jpg
已知,BD,CE分别平分∠ABC,∠ACB.AM⊥CE于M.AN⊥BD于N 求证:MN=1/2(AB+AC-AB)视频
http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=fc1feb7e3887e9504242fb6a20087f7b/1e30e924b899a9010617bf8b1f950a7b0208f569.jpg
已知,BD,CE分别平分∠ABC,∠ACB.AM⊥CE于M.AN⊥BD于N 求证:MN=1/2(AB+AC-AB)视频http://c.hiphotos.baidu.com/zhidao/wh%3D600%2C800/sign=fc1feb7e3887e9504242fb6a20087f7b/1e30e924b899a9010617bf8b1f950a7b0208f569.jpg
证明:延长AM、AN分别交BC于点P、Q,
∵MC是∠ACB的平分线,AM⊥CE
∴AM=MP AC=PC
同理可得:AP=PQ AN=NQ
∵AM=MP AN=NQ
∴MN是△APQ的中位线
∴MN=1/2PQ
又∵PQ=PC+BQ-BC=AB+AC-BC
∴MN=1/2(AB+AC-BC)