{"id":1807,"date":"2025-01-10T13:31:39","date_gmt":"2025-01-10T05:31:39","guid":{"rendered":"https:\/\/muidar.com\/blog\/?p=1807"},"modified":"2026-08-05T23:15:03","modified_gmt":"2026-08-05T15:15:03","slug":"notes-of-similar-figures","status":"publish","type":"post","link":"https:\/\/muidar.com\/blog\/posts\/cmuidar\/notes-of-similar-figures\/","title":{"rendered":"\u76f8\u4f3c\u7684\u4e00\u4e9b\u7b14\u8bb0"},"content":{"rendered":"\n

\u8be5\u7b14\u8bb0\u662f\u5bf9\u8bfe\u4e0a\u6240\u8bb2\u7684\u603b\u7ed3\uff0c\u4e0d\u5168\u4e3a\u76f8\u4f3c\u3002<\/p>\n\n\n\n

\u76f8\u4f3c\u4e09\u89d2\u5f62\u7684\u5224\u5b9a\u65b9\u6cd5\u6709AA\u3001SAS\u3001SSS\u3001HL\uff0c\u503c\u5f97\u6ce8\u610f\u7684\u662f\u548c\u5168\u7b49\u4e00\u6837\uff0cSSA\u4e5f\u662f\u65e0\u6cd5\u5224\u5b9a\u7684\u3002<\/p>\n\n\n\n

\u76f8\u4f3c\u4e09\u89d2\u5f62\u9664\u4e86\u9884\u5907\u5b9a\u7406\u5916\uff0c\u8fd8\u6709\u4ee5\u4e0b\u91cd\u8981\u6027\u8d28\uff1a\u5468\u957f\u6bd4\u3001\u5bf9\u5e94\u8fb9\u4e0a\u7684\u9ad8\u957f\u4e4b\u6bd4\u3001\u5bf9\u5e94\u5143\u7d20\u957f\u5ea6\u4e4b\u6bd4\u7686\u7b49\u4e8e\u76f8\u4f3c\u6bd4\uff1b\u9762\u79ef\u6bd4\u7b49\u4e8e\u76f8\u4f3c\u6bd4\u7684\u5e73\u65b9\u3002\u8fd9\u4e9b\u5c31\u662f\u6700\u57fa\u672c\u7684\u4e86\u3002<\/p>\n\n\n\n

\u4e0b\u9762\u6765\u8bb0\u5f55\u4e00\u4e9b\u6a21\u578b\u5427\u3002<\/p>\n\n\n\n

\u6700\u57fa\u672c\u7684\u5c31\u662f\u6bcd\u5b50\u5f62\uff0c\u5c04\u5f71\u5f62\u662f\u5176\u4e2d\u4e00\u4e2a\u7279\u4f8b\u3002<\/p>\n\n\n\n

\"\"<\/div><\/figure>\n\n\n\n

\u5982\u56fe\uff0c\\bigtriangleup ABC<\/span>\u4e2d\uff0cBC\u4e0a\u6709\u4e00\u70b9D\uff0c\u4e14\\angle CAD=\\angle B<\/span>\u3002\u5219\\bigtriangleup ABC \\sim \\triangle CAD<\/span>\uff0c\u56e0\u6b64AC^2=BC \\cdot CD\u548cAB^2=BC \\cdot BD \\Rightarrow \\frac{AB^2}{AC^2}=\\frac{BD}{CD}=\\frac{S_{\\triangle ABD}}{S_{\\triangle ADC}}<\/span>\u3002<\/p>\n\n\n\n

\u8fd8\u6709\u4e00\u4e2a\u662f\u624b\u62c9\u624b\u3002<\/p>\n\n\n\n

\"\"<\/div><\/figure>\n\n\n\n

\u4e03\u516b\u5e74\u7ea7\u5b66\u4e60\u4e86\u624b\u62c9\u624b\u8bc1\u5168\u7b49\uff0c\u5176\u5b9e\u5176\u4e2d\u8fd8\u6709\u4e24\u5bf9\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u4ee5\u4e92\u63a8\u3002\u5728\u4e0a\u56fe\u4e2d\uff0c\\triangle ABC \\sim \\triangle AB'C' \\Leftrightarrow \\triangle ABB' \\sim \\triangle ACC'<\/span>\u3002\u7279\u522b\u5730\uff0c\u82e5BC'B'<\/span>\u5171\u7ebf\uff0c\u90a3\u4e48ACBC'<\/span>\u5171\u5706\uff0c\u7528\u5185\u5bf9\u89d2\u4e92\u8865\u53ef\u8bc1\uff0c\u53cd\u8fc7\u6765\u4e5f\u662f\u6210\u7acb\u7684\u3002<\/p>\n\n\n\n

\"\"<\/div><\/figure>\n\n\n\n

\u5982\u56fe\u6240\u793a\uff0c\\angle 1= \\angle ABC<\/span>\u662f\\angle 2= \\angle 3<\/span>\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u3002<\/p>\n\n\n\\begin{array}{l}\n\n\\because \\angle 1=\\angle ABC \\\\\n\n\\angle A= \\angle A \\\\\n\n\\therefore \\triangle AED \\sim \\triangle ABC \\\\\n\n\\therefore \\frac{AE}{AB} =\\frac{AD}{AC} \u53c8\\angle A= \\angle A \\\\\n\n\\therefore \\triangle AEB \\sim \\triangle ADC \\\\\n\n\\therefore \\angle 4=\\angle 5 \u53c8\\angle 6=\\angle 7 \\\\\n\n\\therefore \\frac{DF}{EF}= \\frac{BF}{CF} \u53c8\\angle 8=\\angle 9\\\\\n\n\\therefore \\triangle BFC \\sim \\triangle DFE \\\\\n\n\\therefore \\angle 2=\\angle 3\n\n\\end{array}<\/span>\n\n\n\n

\u53cd\u4e4b\u4ea6\u7136\u3002latex\u4e0d\u597d\u7528\uff0c\u5c31\u4e0d\u5199\u4e86\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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