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{ "embedding_dim" : 1024 , "data" : [ { "__id__" : "chunk-a5e3dacee89618f913c4948b6ffe64ec" , "__created_at__" : 1752209869 , "content" : "三角形三边关系的证明\n证明方法如下: \n作下图所示的三角形ABC。在三角形ABC中, [三角不等式](https://zhida.zhihu.com/search?content_id=248217850&content_type=Article&match_order=1&q=%E4%B8%89%E8%A7%92%E4%B8%8D%E7%AD%89%E5%BC%8F&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3NTIzNzg0NDAsInEiOiLkuInop5LkuI3nrYnlvI8iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjoyNDgyMTc4NTAsImNvbnRlbnRfdHlwZSI6IkFydGljbGUiLCJtYXRjaF9vcmRlciI6MSwiemRfdG9rZW4iOm51bGx9.rH6r8SvGmu-I9piEsmZfg2HjbXzUduYclZ2jfA3jZRs&zhida_source=entity)可以表示为|AB|+|BC|> |AC|。\n\nheight=\"2.8183694225721783in\"}\n①延长直线AB至点D, 并使|BD|=|BC|,连接|DC|, 那么三角形BCD为等腰三角形。所以∠BDC=∠BCD。\n②记它们均为α , 根据[欧几里得第五公理](https://zhida.zhihu.com/search?content_id=248217850&content_type=Article&match_order=1&q=%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E7%AC%AC%E4%BA%94%E5%85%AC%E7%90%86&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3NTIzNzg0NDAsInEiOiLmrKflh6Dph4zlvpfnrKzkupTlhaznkIYiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjoyNDgyMTc4NTAsImNvbnRlbnRfdHlwZSI6IkFydGljbGUiLCJtYXRjaF9vcmRlciI6MSwiemRfdG9rZW4iOm51bGx9.ltcWsMYJv-ZzcuBaSjYN69JC8hnIyPMFsfhIlum4yqc&zhida_source=entity), ∠ACD大于角∠ADC(α )。\n③由于∠ACD的对边为AD, ∠ADC(α )的对边为AC, 所以根据大角对大边([几何原本](https://zhida.zhihu.com/search?content_id=248217850&content_type=Article&match_order=1&q=%E5%87%A0%E4%BD%95%E5%8E%9F%E6%9C%AC&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3NTIzNzg0NDAsInEiOiLlh6DkvZXljp_mnKwiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjoyNDgyMTc4NTAsImNvbnRlbnRfdHlwZSI6IkFydGljbGUiLCJtYXRjaF9vcmRlciI6MSwiemRfdG9rZW4iOm51bGx9.Q1rCY0S2bj5Dwp3Fg7xb_VSFESz2_pCUETDybnHANvo&zhida_source=entity)中的命题19)就可以得到|AB|+|BC|=|AB|+|BD|=|AD|> |AC|。" , "full_doc_id" : "doc-a5e3dacee89618f913c4948b6ffe64ec" , "file_path" : "unknown_source" } ] , "matrix" : 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fuLyK1Xm8OKbfvB+dgLwhZ5G9/ZCZvPmhUTwD7wq8JvtzvC8jtby2Lts7YjXxOyEngTyIMGE8nEAUO1coBb1zFky9e5m1PQtN/rqPjlI8kVgiPf9aqj2ocjc8BBTEPA2XLT2DnL87pihHvDhL+LoDSvQ8HriYvVx8ljz4ITE87a//O4r6sLwHngO8YOs/PHeqbTyDHOA8rpAYPbO/8rvv+a68S/ZjvA48xrtrODq9ncrVOxnkp7xABJA8dgXVvN8YE734fJg7yn4evNspCr3BexQ9zMjPuoMcn7yPTgG9j44RPW4ngjzbhDK91Kaguipq3LxI7IE8SdFrvE/lKz3gvWw97AqmOvZXoDwsNG28TLYSPYvfGL3xnkc9hME3u5LYwrwJQ5w89tdAPL4x5TwstMw8sr8xPAjeVDzxnse89A3xvCFnkTy0iUI8NbeVPCOMyjxQigM9TcCzvA==" }