数学初二勾股定理题 初二数学勾股定理题（详细步骤，给20分）
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\u8bbeAD=x\uff0c\u5219CD=12-x
FC²=DF²+CD²=16+(12-x)²
BC²=36
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16+(12-x)²=36+x²
x=124/24=31/6
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x²=16+(12-x)²+36
x=49/6
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36=16+(12-x)²+x²
x²-12x+62=0
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\uff082\uff09 \u5982\u56fe3-158\uff0c\u25b3ABC\u4e2d\uff0c\u2220A=45\u00b0\uff0c\u2220B=30\u00b0\uff0cBC=8\uff0e\u6c42AC\u8fb9\u7684\u957f\uff0e
\u5206\u6790\uff1a\u6dfb\u52a0\u8f85\u52a9\u7ebf\u2014\u2014\u4f5cCD\u22a5AB\u4e8eD\uff0c\u6784\u9020\u542b45\u00b0\uff0c30\u00b0\u89d2\u7684\u76f4\u89d2\u4e09\u89d2\u5f62\u5217\u65b9\u7a0b\u89e3\u51b3\u95ee\u9898\uff0e
\uff083\uff09\u5982\u56fe3-159\uff08a\uff09\uff0c\u5728\u56db\u8fb9\u5f62ABCD\u4e2d\uff0c\u2220B=
\u2220D=90\u00b0\uff0c\u2220C=60\u00b0\uff0cAD=1\uff0cBC=2\uff0c\u6c42AB\uff0cCD\uff0e
\u63d0\u793a\uff1a\u6dfb\u52a0\u8f85\u52a9\u7ebf\u2014\u2014\u5ef6\u957fBA\uff0cCD\u4ea4\u4e8eE\uff0c\u6784\u902030\u00b0\u89d2\u7684Rt\u25b3EAD,Rt\u25b3EBC.\u5229\u7528\u5b83\u4eec\u7684\u6027\u8d28\u6765\u89e3\u51b3\u95ee\u9898\uff08\u89c1\u56fe3-159\uff08b\uff09\uff09.\u6216\u5c06\u56db\u8fb9\u5f62ABCD\u5206\u5272\u6210\u542b30\u00b0\u7684\u76f4\u89d2\u4e09\u89e3\u5f62\u53ca\u77e9\u5f62\u6765\u89e3\u51b3\u95ee\u9898\uff0e\uff08\u89c1\u56fe3-159\uff08c\uff09\uff09
\u7b54\u6848\uff1aAB=23-2\uff0cCD=4-3\uff0e
\uff084\uff09\u5df2\u77e5\uff1a3-160\uff08a\uff09,\u77e9\u5f62ABCD\uff0e\uff08\u56db\u4e2a\u89d2\u662f\u76f4\u89d2\uff09
\u2460P\u4e3a\u77e9\u5f62\u5185\u4e00\u70b9\uff0c\u6c42\u8bc1PA2\uff0b PC2\uff1d PB2\uff0b PD2
\u2461\u63a2\u7d22P\u8fd0\u52a8\u5230AD\u8fb9\u4e0a\uff08\u56fe3\uff0d160\uff08b\uff09\uff09\u3001\u77e9\u5f62ABCD\u5916(\u56fe3\uff0d160\uff08C\uff09\uff09\u65f6\uff0c\u7ed3\u8bba\u662f\u5426\u4ecd\u7136\u6210\u7acb\uff0e
\u5206\u6790\uff1a
\uff081\uff09\u6dfb\u52a0\u8f85\u52a9\u7ebf\u2014\u2014\u8fc7P\u4f5cEF\u22a5BC\u4ea4AD\u5e72E\uff0c\u4ea4BC\u4e8eF\uff0e\u5728\u56db\u4e2a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\u5206\u522b
\u4f7f\u7528\u52fe\u80a1\u5b9a\u7406\uff0e
\uff082\uff09\u53ef\u5c06\u4e09\u4e2a\u9898\u5f52\u7eb3\u6210\u4e00\u4e2a\u547d\u9898\u5982\u4e0b\uff1a
\u77e9\u5f62\u6240\u5728\u5e73\u9762\u4e0a\u4efb\u4e00\u70b9\u5230\u4e0d\u76f8\u90bb\u9876\u70b9\u7684\u8ddd\u79bb\u7684\u5e73\u65b9\u548c\u76f8\u7b49\uff0e
\u56db\u3001\u5e08\u751f\u5171\u540c\u56de\u5fc6\u5c0f\u7ed3
1\uff0e\u52fe\u80a1\u5b9a\u7406\u7684\u5185\u5bb9\u53ca\u8bc1\u660e\u65b9\u6cd5\uff0e
2\uff0e\u52fe\u80a1\u5b9a\u7406\u7684\u4f5c\u7528\uff1a\u5b83\u80fd\u628a\u4e09\u89d2\u5f62\u7684\u5f62\u7684\u7279\u5f81\uff08\u4e00\u89d2\u4e3a90\u00b0\uff09\u8f6c\u5316\u4e3a\u6570\u91cf\u5173\u7cfb\uff0c\u5373\u4e09\u8fb9\u6ee1\u8db3a2+b2=c2.
3\uff0e\u5229\u7528\u52fe\u80a1\u5b9a\u7406\u8fdb\u884c\u6709\u5173\u8ba1\u7b97\u548c\u8bc1\u660e\u65f6\uff0c\u8981\u6ce8\u610f\u5229\u7528\u65b9\u7a0b\u7684\u601d\u60f3\u6c42\u76f4\u89d2\u4e09\u89d2\u5f62\u6709\u5173\u7ebf\u6bb5
\u957f\uff1b\u5229\u7528\u6dfb\u52a0\u8f85\u52a9\u7ebf\u7684\u65b9\u6cd5\u6784\u9020\u76f4\u89d2\u4e09\u89d2\u5f62\u4f7f\u7528\u52fe\u80a1\u5b9a\u7406\uff0e
\u4e94\u3001\u4f5c\u4e1a
1\uff0e \u8bfe\u672c\u7b2c106\u9875\u7b2c2\uff5e8\u9898\uff0e
2\uff0e\u9605\u8bfb\u8bfe\u672c\u7b2c109\u9875\u7684\u8bfb\u4e00\u8bfb\uff1a\u52fe\u80a1\u5b9a\u7406\u7684\u8bc1\u660e\uff0e
\u8bfe\u5802\u6559\u5b66\u8bbe\u8ba1\u8bf4\u660e
\u672c\u6559\u5b66\u8bbe\u8ba1\u97002\u8bfe\u65f6\u5b8c\u6210\uff0e
1\uff0e\u52fe\u80a1\u5b9a\u7406\u63ed\u793a\u4e86\u76f4\u89d2\u4e09\u89d2\u5f62\u4e09\u8fb9\u4e4b\u95f4\u7684\u6570\u91cf\u5173\u7cfb\uff0c\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e00\u4e2a\u91cd\u8981\u6027\u8d28\uff0e\u672c\u6559\u5b66\u8bbe\u8ba1\u5229\u7528\u8ba1\u7b97\u673a\uff08\u51e0\u4f55\u753b\u677f\u8f6f\u4ef6\u52a8\u6001\u663e\u793a\uff09\u7684\u4f18\u8d8a\u6761\u4ef6\uff0c\u63d0\u4f9b\u8db3\u591f\u5145\u5206\u7684\u5178\u578b\u6750\u6599\u2014\u2014\u5f62\u72b6\u5927\u5c0f\u3001\u4f4d\u7f6e\u53d1\u751f\u53d8\u5316\u7684\u5404\u79cd\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u8ba9\u5b66\u751f\u89c2\u5bdf\u5206\u6790\uff0c\u5f52\u7eb3\u6982\u62ec\uff0c\u63a2\u7d22\u51fa\u76f4\u89d2\u4e09\u89d2\u5f62\u4e09\u8fb9\u4e4b\u95f4\u7684\u5173\u7cfb\u5f0f\uff0c\u5e76\u901a\u8fc7\u4e0e\u9510\u89d2\u3001\u949d\u89d2\u4e09\u89d2\u5f62\u7684\u5bf9\u6bd4\uff0c\u5f3a\u8c03\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u8fd9\u4e2a\u7279\u6709\u6027\u8d28\uff0c\u4f53\u73b0\u4e86\u542f\u53d1\u5b66\u751f\u72ec\u7acb\u5206\u6790\u95ee\u9898\u3001\u53d1\u73b0\u95ee\u9898\u3001\u603b\u7ed3\u89c4\u5f8b\u7684\u6559\u5b66\u65b9\u6cd5\uff0e
2\uff0e \u5404\u5b66\u6821\u6839\u636e\u81ea\u5df1\u7684\u6559\u5b66\u6761\u4ef6\u8fd8\u53ef\u4ee5\u91c7\u7eb3\u4ee5\u4e0b\u7c7b\u6bd4\u8054\u60f3\u7684\u63a2\u7d22\u65b9\u5f0f\u6765\u5f15\u5165\u65b0\u8bfe\uff0e
\uff081\uff09\u590d\u4e60\u4e09\u89d2\u5f62\u4e09\u8fb9\u7684\u5173\u7cfb\uff0c\u603b\u7ed3\u51fa\u89c4\u5f8b\uff1a\u8f83\u5c0f\u4e24\u8fb9\u7684\u548c\u5927\u4e8e\u7b2c\u4e09\u8fb9\uff0e
\uff082\uff09\u5f15\u5bfc\u5b66\u751f\u7c7b\u6bd4\u8054\u60f3\uff1a\u8f83\u5c0f\u4e24\u8fb9\u7684\u5e73\u65b9\u548c\u4e0e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\u6709\u4f55\u5927\u5c0f\u5173\u7cfb\u5462\uff1f
\uff083\uff09\u4e3e\u51fa\u4e09\u4e2a\u4e8b\u4f8b\uff08\u89c1\u56fe3\uff0d161\uff08a\uff09\uff08b\uff09\uff08 c\uff09\uff09\uff0e
\u5bf9\u6bd4\u53d1\u73b0\u9510\u89d2\u3001\u949d\u89d2\u4e09\u89d2\u5f62\u4e2d\u4e24\u8f83\u5c0f\u8fb9\u7684\u5e73\u65b9\u548c\u5206\u522b\u5927\u4e8e\u6216\u5c0f\u4e8e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\uff0c\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\u8f83\u5c0f\u4e24\u8fb9\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u7b2c\u4e09\u8fb9\u7684\u5e73\u65b9\uff0e
\uff084\uff09\u7528\u6559\u5177\u6f14\u793a\u56fe3\uff0d151\uff0c\u9a8c\u8bc1\u5bf9\u76f4\u89d2\u4e09\u89d2\u5f62\u6240\u505a\u7684\u731c\u60f3\uff0e
\u6559\u5b66\u76ee\u7684\uff1a1\u3001\u4f1a\u9610\u8ff0\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406
2\u3001\u4f1a\u5e94\u7528\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u5224\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62\u662f\u76f4\u89d2\u4e09\u89d2\u5f62
3\u3001\u80fd\u6b63\u786e\u3001\u7075\u6d3b\u7684\u5e94\u7528\u52fe\u80a1\u5b9a\u7406\u53ca\u52fe\u80a1\u7684\u9006\u5b9a\u7406
\u6559\u5b66\u91cd\u70b9\uff1a\u52fe\u80a1\u5b9a\u7406\u9006\u5b9a\u7406\u7684\u5e94\u7528
\u6559\u5b66\u96be\u70b9\uff1a\u52fe\u80a1\u5b9a\u7406\u9006\u5b9a\u7406\u7684\u8bc1\u660e
\u6559\u5b66\u65b9\u6cd5\uff1a\u8bb2\u7ec3\u7ed3\u5408
\u6559\u5b66\u8fc7\u7a0b\uff1a
\u4e00\u3001\u590d\u4e60\u63d0\u95ee
1\u3001 \u52fe\u80a1\u5b9a\u7406\u7684\u6587\u5b57\u8bed\u8a00
2\u3001 \u52fe\u80a1\u5b9a\u7406\u7684\u51e0\u4f55\u7b26\u53f7\u8bed\u8a00
3\u3001 \u52fe\u80a1\u5b9a\u7406\u7684\u4f5c\u7528
4\u3001 \u586b\u7a7a\uff1a\u5df2\u77e5\u4e00\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u4e24\u8fb9\u662f5\u548c12\uff0c\u5219\u7b2c\u4e09\u8fb9\u7684\u957f\u662f \u3002
\u4e8c\u3001\u5bfc\u5165\u65b0\u8bfe
\u52fe\u80a1\u5b9a\u7406\u662f\u4e00\u4e2a\u547d\u9898\uff0c\u4efb\u4f55\u547d\u9898\u90fd\u6709\u9006\u547d\u9898\uff0c\u5b83\u7684\u9006\u547d\u9898\u662f\u4ec0\u4e48\uff1f
\u4e09\u3001\u8bb2\u89e3\u65b0\u8bfe
\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u7684\u6587\u5b57\u8bed\u8a00\uff1a\u5982\u679c\u4e09\u89d2\u5f62\u7684\u4e09\u8fb9\u957f\uff1aa\u3001b\u3001c\u6709\u5173\u7cfb\uff0ca2+b2=c2\uff0c\u90a3\u4e48\u8fd9\u4e2a\u4e09\u89d2\u5f62\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\u3002
\u547d\u9898\u6709\u771f\u5047\u4e4b\u5206\uff0c\u5b83\u662f\u5426\u4e3a\u771f\u547d\u9898\uff0c\u9996\u5148\u5fc5\u987b\u8bc1\u660e\u3002
\u5df2\u77e5\uff1a\u5728\u0394ABC\u4e2d\uff0cAB=c\uff0cBC=a\uff0cCA=b\uff0c\u5e76\u4e14a2+b2=c2
\u6c42\u8bc1\uff1a\u2220C=90º
\u5206\u6790\uff1a\u8bc1\u660e\u4e00\u4e2a\u89d2\u4e3a90º\uff0c\u53ef\u4ee5\u8bc1AC\u22a5BC
\u4e5f\u53ef\u4ee5\u5229\u7528\u4e66\u672c\u4e0a\u7684\u65b9\u6cd5\u8bc1\u660e\uff0c\u81ea\u5b66
\u901a\u8fc7\u8bc1\u660e\uff0c\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u547d\u9898\u662f\u4e2a\u771f\u547d\u9898\uff0c\u5373\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u3002
\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u7684\u51e0\u4f55\u7b26\u53f7\u8bed\u8a00\uff1a\u5728\u0394ABC\u4e2d\u2235 a2+b2=c2 \uff08\u6216c2\uff0da2 = b2 \uff09
\u2234\u2220C=90º\uff08\u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\uff09
\u5f3a\u8c03\uff1a\u53ea\u8981\u6ee1\u8db3\u4e0a\u8ff0\u5173\u7cfb\uff0c\u5b83\u5fc5\u5b9a\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u4e14\u8f83\u957f\u7684\u8fb9\u662f\u659c\u8fb9\uff0c\u5b83\u6240\u5bf9\u7684\u89d2\u662f\u76f4\u89d2\u3002
\u4f8b\u5982\uff1a\u4e09\u8fb9\u957f\u5206\u522b\u4e3a3\u30014\u30015\uff0c\u80fd\u5426\u7ec4\u6210\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c5\u300112\u300113\u5462\uff1f9\u300140\u300141\u5462\uff1f
\u52fe\u80a1\u6570\uff1a\u80fd\u591f\u6210\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e09\u6761\u8fb9\u957f\u7684\u4e09\u4e2a\u6b63\u6574\u6570\uff0c\u79f0\u4e3a\u52fe\u80a1\u6570\uff08\u6216\u52fe\u80a1\u5f26\u6570\uff09
\u4e66\u672c102\u2014103\u9875\uff0c\u5212\u51fa\u5b9a\u4e49\uff0c\u5b8c\u6210\u4f5c\u4e1a103\u98751\u30013
\u4f8b1 \u0394ABC\u7684\u4e09\u8fb9\u5206\u522b\u4e3a\u4e0b\u5217\u5404\u7ec4\u503c\uff0c\u80fd\u7ec4\u6210\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u6253\u201c\u221a\u201d\uff0c\u5e76\u6307\u51fa\u54ea\u4e2a\u662f\u76f4\u89d2\uff0c\u5426\u5219\u6253\u201c\u00d7\u201d
\u2474a=1\u3001b= \u3001c=1
\u2475a=1.2\u3001b=1.6\u3001c=2
\u2476a:b:c=2: :2
\u2477a=n2-1\u3001b=2n\u3001c= n2+1(n\uff1e1)
\u2478a=2n2+1\u3001b=2n2+2n\u3001c=2mn(m\uff1en)m\u3001n\u4e3a\u6b63\u6574\u6570
\u89e3\u2474 \u223512+12=\uff08 \uff092 \u2234 \u0394ABC\u662f\u4ee5\u2220B\u4e3a\u76f4\u89d2\u7684\u4e09\u89d2\u5f62
\u2475 \u223522-1.62=(2+1.6)(2-1.6)=1.44=\uff081.2\uff092
\u2234 \u0394ABC\u662f\u4ee5\u2220B\u4e3a\u76f4\u89d2\u7684\u4e09\u89d2\u5f62
\u2476\u2477\u2478\u89e3\u7565\u3002
\u5f3a\u8c03\uff1a\u5bf9\u4e8e\u6570\u5b57\u8f83\u5927\uff0c\u53ef\u4ee5\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\uff0c\u8fbe\u5230\u7b80\u4fbf\u8fd0\u7b97\u3002
\u4f8b2 \u5df2\u77e5\uff1a\u5982\u56fe\uff0cAD=3\uff0cAB=4\uff0c\u2220BAD=90º\uff0cBC=12\uff0cCD=13\uff0c
\u6c42\u56db\u8fb9\u5f62ABCD\u7684\u9762\u79ef.
\u5206\u6790\uff1a\u8fde\u7ed3BD\uff0c\u6c42\u51faBD=5\uff0c
\u2235BD2+BC2=CD2 \u2234\u2220CBD=90º
\u2234\u56db\u8fb9\u5f62ABCD\u7684\u9762\u79ef=\u0394ABD\u7684\u9762\u79ef+\u0394BD\u7684\u9762\u79ef
\u89e3\uff1a\u7565
\u4f8b2 \u5df2\u77e5\uff1a\u5982\u56fe\uff0c\u5728\u0394ABC\u4e2d\uff0cCD\u662fAB\u8fb9\u4e0a\u7684\u9ad8\uff0c\u4e14CD2=AD2•BD
\u6c42\u8bc1\uff1a\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62
\u5206\u6790\uff1a\u8981\u8bc1\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62
\u53ea\u8981\u8bc1AC2+BC2=AB2
\u5728Rt\u0394ACD\u4e2d\uff0c\u2235\u2220ACD=90º
\u2234AC2=AD2+CD2
\u540c\u7406\u53ef\u8bc1\uff0cBC2=CD2+BD2
\u2234AC2 + BC2 = AD2+2 CD2+BD2
=\uff08AD+BD\uff092
\u2234\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62
\u8bf7\u5b66\u751f\u81ea\u5df1\u5b8c\u6210\u8bc1\u660e\u8fc7\u7a0b\u3002
\u4e09\u3001\u8bfe\u5802\u5c0f\u7ed3
1\u3001 \u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u5224\u5b9a\u5b9a\u7406\uff0c\u52fe\u80a1\u5b9a\u7406\u4e3a\u6027\u8d28\u5b9a\u7406\uff0c\u4ed6\u4eec\u4e92\u4e3a\u9006\u5b9a\u7406
2\u3001 \u52fe\u80a1\u5b9a\u7406\u7684\u9006\u5b9a\u7406\u7684\u4f5c\u7528\u662f\u7528\u6765\u5224\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u4e3a\u76f4\u89d2\u4e09\u89d2\u5f62\uff1f
由题意可知
以AC为直径的半圆面积为：（AC/2)^2*(π/2)
以BC为直径的半圆面积为：（BC/2)^2*(π/2)
以AB为直径的半圆面积为：（AB/2)^2*(π/2)
又∵S阴影=S半圆AC+S半圆CB-S半圆AB+S△ABC
∴原式=（AC/2)^2*(π/2)+（BC/2)^2*(π/2)+（AB/2)^2*(π/2)+20
=（（AC/2)^2+(BC/2)^2+（AB/2)^2)*(π/2)+20
=((AC^2+BC^2-AB^2)/4)+20
由勾股定理得AC^2+BC^2=AB^2
即AC^2+BC^2-AB^2=0,带入原式子得
原式=（0/4)+20
=20
∴S阴影=20cm^2
答：——————
设AB=c,AC=b,bc=a则a*2+b*2=c*2 a*2+b*2-c*2=0
s=pi(a/2)*2+pi(b/2)*2-pi(c/2)*2+s ABC=pi(a*2+b*2-c*2)/4+20=20
呃...... 这个图在哪啊
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