【急急急！！】关于三角形的数学题。初一数学。高悬赏。在线等。 ,八年级上册数学几何三角形题目。高悬赏
\u521d\u4e00\u6570\u5b6620\u9053\u8bc1\u660e\u9898 \u6709\u56fe \u6709\u7b54\u6848 \u8dea\u6c42\uff0c\u6ca1\u60ac\u8d4f\u4e86\uff0c\u6211\u6709\u6025\u7528\u3002\u56fe\u7247\u53d1\u4e0d\u4e0a\u6765\uff0c\u770b\u53c2\u8003\u8d44\u6599\u91cc\u7684
1 \u5982\u56fe\uff0cAB\u22a5BC\u4e8eB\uff0cEF\u22a5AC\u4e8eG\uff0cDF\u22a5AC\u4e8eD\uff0cBC=DF\u3002\u6c42\u8bc1\uff1aAC=EF\u3002
2 \u5df2\u77e5AC\u5e73\u5206\u89d2BAD\uff0cCE\u5782\u76f4AB\u4e8eE\uff0c CF\u5782\u76f4AD\u4e8eF\uff0c\u4e14BC=CD
\uff081\uff09\u6c42\u8bc1\uff1a\u25b3BCE\u5168\u7b49\u25b3DCF
3.
\u5982\u56fe\u6240\u793a\uff0c\u8fc7\u4e09\u89d2\u5f62ABC\u7684\u9876\u70b9A\u5206\u522b\u4f5c\u4e24\u5e95\u89d2\u89d2B\u548c\u89d2C\u7684\u5e73\u5206\u7ebf\u7684\u5782\u7ebf\uff0cAD\u5782\u76f4\u4e8eBD\u4e8eD\uff0cAE\u5782\u76f4\u4e8eCE\u4e8eE\uff0c\u6c42\u8bc1\uff1aED||BC.
4.
\u5df2\u77e5\uff0c\u5982\u56fe\uff0cPB\u3001PC\u5206\u522b\u662f\u25b3ABC\u7684\u5916\u89d2\u5e73\u5206\u7ebf\uff0c\u4e14\u76f8\u4ea4\u4e8e\u70b9P\u3002
\u6c42\u8bc1\uff1a\u70b9P\u5728\u2220A\u7684\u5e73\u5206\u7ebf\u4e0a\u3002
\u56de\u7b54\u4eba\u7684\u8865\u5145 2010-07-19 00:10 1.\u5728\u4e09\u89d2\u5f62ABC\u4e2d,\u89d2ABC\u4e3a60\u5ea6,AD\u3001CE\u5206\u522b\u5e73\u5206 \u89d2BAC \u89d2ACB,\u8bd5\u731c\u60f3,AC\u3001AE\u3001CD\u6709\u600e\u4e48\u6837\u7684\u6570\u91cf\u5173\u7cfb
2.\u628a\u7b49\u8fb9\u4e09\u89d2\u5f62\u6bcf\u8fb9\u4e09\u7b49\u5206,\u7ecf\u5176\u5411\u5916\u957f\u51fa\u4e00\u4e2a\u8fb9\u957f\u4e3a\u539f\u6765\u4e09\u5206\u4e4b\u4e00\u7684\u5c0f\u7b49\u8fb9\u4e09\u89d2\u5f62,\u79f0\u4e3a\u4e00\u6b21\u751f\u957f,\u5982\u751f\u957f\u4e09\u6b21,\u5f97\u5230\u7684\u591a\u8fb9\u5f62\u9762\u79ef\u662f\u539f\u4e09\u89d2\u5f62\u9762\u79ef\u7684\u51e0\u500d
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3.\u8bc1\u660e\uff1a\u5bf9\u4e8e\u4efb\u610f\u4e09\u89d2\u5f62\uff0c\u4e00\u5b9a\u5b58\u5728\u4e24\u8fb9a\u3001b\uff0c\u6ee1\u8db3a\u6bd4b\u5927\u4e8e\u7b49\u4e8e1\uff0c\u5c0f\u4e8e2\u5206\u4e4b\u68395\u52a01
4.\u5df2\u77e5\u25b3ABC\u7684\u4e09\u6761\u9ad8\u4ea4\u4e8e\u5782\u5fc3O\uff0c\u5176\u4e2dAB=a\uff0cAC=b,\u2220BAC=\u03b1\u3002\u8bf7\u7528\u53ea\u542ba\u3001b\u3001\u03b1\u4e09\u4e2a\u5b57\u6bcd\u7684\u5f0f\u5b50\u8868\u793aAO\u7684\u957f\uff08\u4e09\u4e2a\u5b57\u6bcd\u4e0d\u4e00\u5b9a\u5168\u90e8\u7528\u5b8c\uff0c\u4f46\u4e00\u5b9a\u4e0d\u80fd\u7528\u5176\u5b83\u5b57\u6bcd\uff09\u3002
5.\u8bbe\u6240\u6c42\u76f4\u7ebf\u4e3ay=kx+b (k,b\u4e3a\u5e38\u6570.k\u4e0d\u7b49\u4e8e0). \u5219\u5176\u5fc5\u8fc7x-y+2=0\u4e0ex+2y-1=0\u7684\u4ea4\u70b9(-1,1).\u6240\u4ee5b=k+1,\u5373\u6240\u6c42\u76f4\u7ebf\u4e3ay=kx+k+1 (1) \u8fc7\u76f4\u7ebfx-y+2=0\u4e0eY\u8f74\u7684\u4ea4\u70b9(0,2)\u4e14\u5782\u76f4\u4e8ex-y+2=0\u7684\u76f4\u7ebf\u4e3ay=-x+2 (2). \u76f4\u7ebf(2)\u4e0e \u76f4\u7ebf(1)\u7684\u4ea4\u70b9\u4e3aA,\u76f4\u7ebf(2)\u4e0e \u76f4\u7ebfx+2y-1=0\u7684\u4ea4\u70b9\u4e3aB,\u5219AB\u7684\u4e2d\u70b9\u4e3a(0,2),\u7531\u7ebf\u6bb5\u4e2d\u70b9\u516c\u5f0f\u53ef\u6c42k.
6. \u5728\u4e09\u89d2\u5f62ABC\u4e2d,\u89d2ABC=60,\u70b9P\u662f\u4e09\u89d2ABC\u5185\u7684\u4e00\u70b9,\u4f7f\u5f97\u89d2APB=\u89d2BPC=\u89d2CPA,\u4e14PA=8 PC =6\u5219PB= 2 P\u662f\u77e9\u5f62ABCD\u5185\u4e00\u70b9\uff0cPA=3 PB= 4 PC=5 \u5219PD= 3 \u4e09\u89d2\u5f62ABC\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u89d2C=90 O\u662f\u4e09\u89d2\u5f62\u5185\u4e00\u70b9\uff0cO\u70b9\u5230\u4e09\u89d2\u5f62\u5404\u8fb9\u7684\u8ddd\u79bb\u90fd\u7b49\u4e8e1\uff0c\u5c06\u4e09\u89d2\u5f62ABC\u9976\u70b9O\u987a\u65f6\u9488\u65cb\u8f6c45\u5ea6\u5f97\u4e09\u89d2\u5f62A1B1C1 \u4e24\u4e09\u89d2\u5f62\u7684\u516c\u5171\u90e8\u5206\u4e3a\u591a\u8fb9\u5f62KLMNPQ\uff0c 1\uff09\u8bc1\u660e\uff1a\u4e09\u89d2\u5f62AKL \u4e09\u89d2\u5f62BMN \u4e09\u89d2\u5f62CPQ \u90fd\u662f\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62 2\uff09\u6c42\u4e09\u89d2\u5f62ABC\u4e0e\u4e09\u89d2\u5f62A1B1C1\u516c\u5171\u90e8\u5206\u7684\u9762\u79ef\u3002
\u5df2\u77e5\u4e09\u89d2\u5f62ABC,a,b,c\u5206\u522b\u4e3a\u4e09\u8fb9. \u6c42\u8bc1:\u4e09\u89d2\u5f62\u4e09\u8fb9\u7684\u5e73\u65b9\u548c\u5927\u4e8e\u7b49\u4e8e16\u500d\u7684\u6839\u53f73 (\u5373:a2+b2+c2\u5927\u4e8e\u7b49\u4e8e16\u500d\u7684\u6839\u53f73)
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1\uff0e\u5982\u679c\u03b1\u548c\u03b2\u662f\u540c\u65c1\u5185\u89d2\uff0c\u4e14\u03b1=55\u00b0\uff0c\u5219\u03b2\u7b49\u4e8e\uff08 \uff09
(A)55\u00b0 \uff08B\uff09125\u00b0 \uff08C\uff0955\u00b0\u6216125\u00b0 \uff08D\uff09\u65e0\u6cd5\u786e\u5b9a
2\uff0e\u5982\u56fe19-2-\uff082\uff09
AB\u2016CD\u82e5\u22202\u662f\u22201\u76842\u500d\uff0c\u5219\u22202\u7b49\u4e8e\uff08 \uff09
\uff08A\uff09 60\u00b0\uff08B\uff0990\u00b0\uff08C\uff09120\u00b0 \uff08D\uff09150
3\uff0e\u5982\u56fe19-2-\uff083\uff09
\u22201+\u22202=180\u00b0\uff0c\u22203=110\u00b0\uff0c\u5219\u22204\u5ea6\u6570\uff08 \uff09
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4\uff0e\u5982\u56fe19-2-\uff083\uff09
\u22201+\u22202=180\u00b0\uff0c\u22203=110\u00b0\uff0c\u5219\u22201\u7684\u5ea6\u6570\u662f\uff08 \uff09
\uff08A\uff0970\u00b0 \uff08B\uff09110\u00b0
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5\uff0e\u5982\u56fe19-2\uff085\uff09\uff0c
\u5df2\u77e5\u22201=\u22202\uff0c\u82e5\u8981\u4f7f\u22203=\u22204\uff0c\u5219\u9700\uff08 \uff09
\uff08A\uff09\u22201=\u22202 \uff08B\uff09\u22202=\u22203
\uff08C\uff09\u22201=\u22204 \uff08D\uff09AB\u2016CD
6\uff0e\u5982\u56fe19-2-\uff086\uff09\uff0c
AB\u2016CD\uff0c\u22201=\u2220B\uff0c\u22202=\u2220D\uff0c\u5219\u2220BED\u4e3a\uff08 \uff09
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7\uff0e\u82e5\u4e24\u4e2a\u89d2\u7684\u4e00\u8fb9\u5728\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a\uff0c\u53e6\u4e00\u8fb9\u76f8\u4e92\u5e73\u884c\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u89d2\u7684\u5173\u7cfb\u662f\uff08\uff09
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8\uff0e\u5982\u56fe19-2-\uff088\uff09AB\u2016CD\uff0c\u2220\u03b1=\uff08\uff09
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\u7b54\u6848\uff1a1.D 2. C 3. C 4. C 5. D 6. B 7. D 8. B
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1\uff0e\u4e24\u4e2a\u89d2\u7684\u548c\u4e0e\u8fd9\u4e24\u89d2\u7684\u5dee\u4e92\u8865\uff0c\u5219\u8fd9\u4e24\u4e2a\u89d2\uff08 \uff09
A\uff0e\u4e00\u4e2a\u662f\u9510\u89d2\uff0c\u4e00\u4e2a\u662f\u949d\u89d2 B\uff0e\u90fd\u662f\u949d\u89d2
C\uff0e\u90fd\u662f\u76f4\u89d2 D\uff0e\u5fc5\u6709\u4e00\u4e2a\u76f4\u89d2
2\uff0e\u5982\u679c\u22201\u548c\u22202\u662f\u90bb\u8865\u89d2\uff0c\u4e14\u22201\uff1e\u22202\uff0c\u90a3\u4e48\u22202\u7684\u4f59\u89d2\u662f\uff08 \uff09
3\uff0e\u4e0b\u5217\u8bf4\u6cd5\u6b63\u786e\u7684\u662f \uff08 \uff09
A\uff0e\u4e00\u6761\u76f4\u7ebf\u7684\u5782\u7ebf\u6709\u4e14\u53ea\u6709\u4e00\u6761
B\uff0e\u8fc7\u5c04\u7ebf\u7aef\u70b9\u4e0e\u5c04\u7ebf\u5782\u76f4\u7684\u76f4\u7ebf\u53ea\u6709\u4e00\u6761
C\uff0e\u5982\u679c\u4e24\u4e2a\u89d2\u4e92\u4e3a\u8865\u89d2\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u89d2\u4e00\u5b9a\u662f\u90bb\u8865\u89d2
D\uff0e\u8fc7\u76f4\u7ebf\u5916\u548c\u76f4\u7ebf\u4e0a\u7684\u4e24\u4e2a\u5df2\u77e5\u70b9\uff0c\u505a\u5df2\u77e5\u76f4\u7ebf\u7684\u5782\u7ebf
4\uff0e\u5728\u540c\u4e00\u5e73\u9762\u5185\uff0c\u4e24\u6761\u4e0d\u91cd\u5408\u76f4\u7ebf\u7684\u4f4d\u7f6e\u5173\u7cfb\u53ef\u80fd\u6709\uff08 \uff09
A\uff0e\u5e73\u884c\u6216\u76f8\u4ea4 B\uff0e\u5782\u76f4\u6216\u5e73\u884c
C\uff0e\u5782\u76f4\u6216\u76f8\u4ea4 D\uff0e\u5e73\u884c\u3001\u5782\u76f4\u6216\u76f8\u4ea4
5\uff0e\u4e0d\u76f8\u90bb\u7684\u4e24\u4e2a\u76f4\u89d2\uff0c\u5982\u679c\u5b83\u4eec\u6709\u4e00\u6761\u516c\u5171\u8fb9\uff0c\u90a3\u4e48\u53e6\u4e00\u8fb9\u4e92\u76f8\uff08 \uff09
A\uff0e\u5e73\u884c B\uff0e\u5782\u76f4
C\uff0e\u5728\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a D\uff0e\u6216\u5e73\u884c\u3001\u6216\u5782\u76f4\u3001\u6216\u5728\u540c\u4e00\u6761\u76f4\u7ebf\u4e0a
\u7b54\u6848\uff1a1\uff0eD 2\uff0eC 3\uff0eB 4\uff0eA 5\uff0eA\u56de\u7b54\u4eba\u7684\u8865\u5145 2010-07-19 00:21 1.\u5982\u56fe\u6240\u793a\uff0c\u4e00\u53ea\u8001\u9f20\u6cbf\u7740\u957f\u65b9\u5f62\u9003\u8dd1\uff0c\u4e00\u53ea\u82b1\u732b\u540c\u65f6\u4eceA\u70b9\u671d\u53e6\u4e00\u4e2a\u65b9\u5411\u6cbf\u7740\u957f\u65b9\u5f62\u53bb\u6355\u6349\uff0c\u7ed3\u679c\u5728\u8dddB\u70b930cm\u7684C\u70b9\u5904\u6349\u4f4f\u4e86\u8001\u9f20\u3002\u5df2\u77e5\u8001\u9f20\u4e0e\u732b\u7684\u901f\u5ea6\u4e4b\u6bd4\u4e3a11\uff1a14\uff0c\u6c42\u957f\u65b9\u5f62\u7684\u5468\u957f\u3002\u8bbe\u5468\u957f\u4e3aX.\u5219A\u5230B\u7684\u8ddd\u79bb\u4e3aX/2;X/2-30:X/2+30=11:14X=500 cm\u5982\u56fe\uff0c\u68af\u5f62ABCD\u4e2d\uff0cAD\u5e73\u884cBC\uff0c\u2220A=2\u2220C\uff0cAD=10cm\uff0cBC=25cm\uff0c\u6c42AB\u7684\u957f\u89e3\uff1a\u8fc7\u70b9A\u4f5cAB\u2016DE\u3002\u2235AB\u2016DE\uff0cAD\u2016BC\u2234\u56db\u8fb9\u5f62ADEB\u662f\u5e73\u4fe1\u56db\u8fb9\u5f62\u2234AB=DE\uff0cAD=BE\u2235\u2220DEB\u662f\u4e09\u89d2\u5f62DEC\u7684\u5916\u89d2\u2234\u2220DEB=\u2220CDE+\u2220C\u2235\u56db\u8fb9\u5f62ADEB\u662f\u5e73\u4fe1\u56db\u8fb9\u5f62\u2234\u2220A=\u2220DEB\u53c8\u2235\u2220A=2\u2220C\uff0c\u2220DEB=\u2220CDE+\u2220C\u2234\u2220CDE+\u2220C\u2234DE=CE\u2235AD=10\uff0cBC=25\uff0cAD=BE\u2234CE=15=DE=AB\u5982\u56fe\uff1a\u7b49\u8170\u4e09\u89d2\u5f62ABCD\u4e2d\uff0cAD\u5e73\u884cBC\uff0cBD\u22a5DC\uff0c\u4e14\u22201=\u22202\uff0c\u68af\u5f62\u7684\u5468\u957f\u4e3a30CM\uff0c\u6c42AB\u3001BC\u7684\u957f\u3002\u56e0\u4e3a\u7b49\u8170\u68af\u5f62ABCD\uff0c\u6240\u4ee5\u89d2ABC=\u89d2C\uff0cAB=CD\uff0cAD//BC\u6240\u4ee5\u89d2ADB=\u89d22\uff0c\u53c8\u89d21=\u89d22\uff0c\u6240\u4ee5\u89d21=\u89d22=\u89d2ADB\uff0c\u800c\u89d2ABC=\u89d2C=\u89d21+\u89d22\u4e14\u89d22=\u89d2ADB\u6240\u4ee5\u89d2ADB+\u89d2C=90\u5ea6\uff0c\u6240\u4ee5\u6709\u89d21+\u89d22+\u89d2ADB=90\u5ea6\u6240\u4ee5\u89d22=30\u5ea6\u56e0\u6b64BC=2CD=2AB\u6240\u4ee5\u5468\u957f\u4e3a5AB=30\u6240\u4ee5AB=6\uff0cBC=12 \u56de\u7b54\u4eba\u7684\u8865\u5145 2010-07-03 11:25 \u5982\u56fe\uff1a\u6b63\u65b9\u5f62ABCD\u7684\u8fb9\u957f\u4e3a4\uff0cG\u3001F\u5206\u522b\u5728DC\u3001CB\u8fb9\u4e0a\uff0cDG=GC=2\uff0cCF=1.\u6c42\u8bc1\uff1a\u22201=\u22202\uff08\u8981\u4e24\u79cd\u89e3\u6cd5 \u63d0\u793a\u4e00\u79cd\u601d\u8def\uff1a\u8fde\u63a5\u5e76\u5ef6\u957fFG\u4ea4AD\u7684\u5ef6\u957f\u7ebf\u4e8eK\uff09
1.\u8fde\u63a5\u5e76\u5ef6\u957fFG\u4ea4AD\u7684\u5ef6\u957f\u7ebf\u4e8eK\u2220KGD=\u2220FGC \u2220GDK=\u2220GCF BG=CG \u25b3CGF\u224c\u25b3DGK GF=GKAB=4 BF=3 AF=5 AB=4+1=5 AB=AF AG=AG \u25b3AGF\u224c\u25b3AGK \u22201=\u22202
2.\u5ef6\u957fAC\u4ea4BC\u5ef6\u957f\u7ebf\u4e0eE\u2220ADG=\u2220ECG \u2220AGD=\u2220EGC DG=GC \u25b3ADG\u224c\u25b3EGF \u22201=\u2220E AD=CEAF=5 EF=1+4=5 \u22202=\u2220E \u6240\u4ee5\u22201=\u22202\u5982\u56fe\uff0c\u56db\u8fb9\u5f62ABCD\u662f\u5e73\u884c\u56db\u8fb9\u5f62\uff0cBE\u5e73\u884cDF\uff0c\u5206\u522b\u4ea4AC\u4e8eE\u3001F\u8fde\u63a5ED\u3001BF \u6c42\u8bc1\u22201=\u22202
\u7b54\u6848\uff1a\u8bc1\u4e09\u89d2\u5f62BFE \u5168\u7b49 \u4e09\u89d2\u5f62DEF\u3002 \u56e0\u4e3aFE=EF\uff0c\u89d2BEF=90\u5ea6=\u89d2DFE\uff0cDF=BE\uff08\u5168\u7b49\u4e09\u89d2\u5f62\u7684\u5bf9\u5e94\u9ad8\u76f8\u7b49\uff09\u3002 \u6240\u4ee5\u4e09\u89d2\u5f62BFE \u5168\u7b49 \u4e09\u89d2\u5f62DEF\u3002 \u6240\u4ee5\u22201\u7b49\u4e8e\u22202\uff08\u5168\u7b49\u4e09\u89d2\u5f62\u5bf9\u5e94\u89d2\u76f8\u7b49\uff09
\u5c31\u7ed9\u8fd9\u4e48\u591a\u5427~~N\u7d2f~\uff01\uff01\u56de\u7b54\u4eba\u7684\u8865\u5145 2010-07-19 00:34 1\u5df2\u77e5\u0394ABC\uff0cAD\u662fBC\u8fb9\u4e0a\u7684\u4e2d\u7ebf\u3002E\u5728AB\u8fb9\u4e0a\uff0cED\u5e73\u5206\u2220ADB\u3002F\u5728AC\u8fb9\u4e0a\uff0cFD\u5e73\u5206\u2220ADC\u3002\u6c42\u8bc1\uff1aBE+CF\uff1eEF\u3002
2\u5df2\u77e5\u0394ABC\uff0cBD\u662fAC\u8fb9\u4e0a\u7684\u9ad8\uff0cCE\u662fAB\u8fb9\u4e0a\u7684\u9ad8\u3002F\u5728BD\u4e0a\uff0cBF=AC\u3002G\u5728CE\u5ef6\u957f\u7ebf\u4e0a\uff0cCG=AB\u3002\u6c42\u8bc1\uff1aAG=AF\uff0cAG\u22a5AF\u3002
3\u5df2\u77e5\u0394ABC\uff0cAD\u662fBC\u8fb9\u4e0a\u7684\u9ad8\uff0cAD=BD\uff0cCE\u662fAB\u8fb9\u4e0a\u7684\u9ad8\u3002AD\u4ea4CE\u4e8eH\uff0c\u8fde\u63a5BH\u3002\u6c42\u8bc1\uff1aBH=AC\uff0cBH\u22a5AC\u3002
4\u5df2\u77e5\u0394ABC\uff0cAD\u662fBC\u8fb9\u4e0a\u7684\u4e2d\u7ebf\uff0cAB=2\uff0cAC=4\uff0c\u6c42AD\u7684\u53d6\u503c\u8303\u56f4\u3002
5\u5df2\u77e5\u0394ABC\uff0cAB\uff1eAC\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cP\u662fAD\u4e0a\u4efb\u610f\u4e00\u70b9\u3002\u6c42\u8bc1\uff1aAB-AC\uff1ePB-PC\u3002
6\u5df2\u77e5\u0394ABC\uff0cAB\uff1eAC\uff0cAE\u662f\u5916\u89d2\u5e73\u5206\u7ebf\uff0cP\u662fAE\u4e0a\u4efb\u610f\u4e00\u70b9\u3002\u6c42\u8bc1\uff1aPB+PC\uff1eAB+AC\u3002
7\u5df2\u77e5\u0394ABC\uff0cAB\uff1eAC\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\u3002\u6c42\u8bc1\uff1aBD\uff1eDC\u3002
8\u5df2\u77e5\u0394ABD\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAB=AD\u3002\u0394ACE\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAC=AE\u3002\u8fde\u63a5CD\uff0cBE\u3002\u6c42\u8bc1\uff1aCD=BE\uff0cCD\u22a5BE\u3002
9\u5df2\u77e5\u0394ABC\uff0cD\u662fAB\u4e2d\u70b9\uff0cE\u662fAC\u4e2d\u70b9\uff0c\u8fde\u63a5DE\u3002\u6c42\u8bc1\uff1aDE\u2016BC\uff0c2DE=BC\u3002
10\u5df2\u77e5\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAB=AC\u3002\u8fc7A\u4f5c\u76f4\u7ebfAN\uff0cBD\u22a5AN\u4e8eD\uff0cCE\u22a5AN\u4e8eE\u3002\u6c42\u8bc1\uff1aDE=BD-CE\u3002
\u7b49\u5f62 2
1\u5df2\u77e5\u56db\u8fb9\u5f62ABCD\uff0cAB=BC\uff0cAB\u22a5BC\uff0cDC\u22a5BC\u3002E\u5728BC\u8fb9\u4e0a\uff0cBE=CD\u3002AE\u4ea4BD\u4e8eF\u3002\u6c42\u8bc1\uff1aAE\u22a5BD\u3002
2\u5df2\u77e5\u0394ABC\uff0cAB\uff1eAC\uff0cBD\u662fAC\u8fb9\u4e0a\u7684\u4e2d\u7ebf\uff0cCE\u22a5BD\u4e8eE\uff0cAF\u22a5BD\u5ef6\u957f\u7ebf\u4e8eF\u3002\u6c42\u8bc1\uff1aBE+BF=2BD\u3002
3\u5df2\u77e5\u56db\u8fb9\u5f62ABCD\uff0cAB\u2016CD\uff0cE\u5728BC\u4e0a\uff0cAE\u5e73\u5206\u2220BAD\uff0cDE\u5e73\u5206\u2220ADC\uff0c\u82e5AB=2\uff0cCD=3\uff0c\u6c42AD\u3002
4\u5df2\u77e5\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAC=BC\uff0cBE\u662f\u89d2\u5e73\u5206\u7ebf\uff0cAF\u22a5BE\u5ef6\u957f\u7ebf\u4e8eF\u3002\u6c42\u8bc1\uff1aBE=2AF\u3002
5\u5df2\u77e5\u0394ABC\uff0c\u2220ACB=90\u00b0\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cCE\u662fAB\u8fb9\u4e0a\u7684\u9ad8\uff0cCE\u4ea4AD\u4e8eF\uff0cFG\u2016AB\u4ea4BC\u4e8eG\u3002\u6c42\u8bc1\uff1aCD=BG\u3002
6\u5df2\u77e5\u0394ABC\uff0c\u2220ACB=90\u00b0\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cCE\u662fAB\u8fb9\u4e0a\u7684\u9ad8\uff0cCE\u4ea4AD\u4e8eF\uff0cFG\u2016BC\u4ea4AB\u4e8eG\u3002\u6c42\u8bc1\uff1aAC=AG\u3002
7\u5df2\u77e5\u56db\u8fb9\u5f62ABCD\uff0cAB\u2016CD\uff0c\u2220D=2\u2220B\uff0c\u82e5AD=m\uff0cDC=n\uff0c\u6c42AB\u3002
8\u5df2\u77e5\u0394ABC\uff0cAC=BC\uff0cCD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cM\u4e3aCD\u4e0a\u4e00\u70b9\uff0cAM\u4ea4BC\u4e8eE\uff0cBM\u4ea4AC\u4e8eF\u3002\u6c42\u8bc1\uff1a\u0394CME\u224c\u0394CMF\uff0cAE=BF\u3002
9\u5df2\u77e5\u0394ABC\uff0cAC=2AB\uff0c\u2220A=2\u2220C\uff0c\u6c42\u8bc1\uff1aAB\u22a5BC\u3002
10\u5df2\u77e5\u0394ABC\uff0c\u2220B=60\u00b0\u3002AD\uff0cCE\u662f\u89d2\u5e73\u5206\u7ebf\uff0c\u6c42\u8bc1\uff1aAE+CD=AC
\u5168\u7b49\u5f62 4
1\u5df2\u77e5\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAB=AC\uff0c\u0394ADE\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAD=AE\uff0c\u8fde\u63a5CD\uff0cBE\uff0cM\u662fBE\u4e2d\u70b9\uff0c\u6c42\u8bc1\uff1aAM\u22a5CD\u3002
2\u5df2\u77e5\u0394ABC\uff0cAD\uff0cBE\u662f\u9ad8\uff0cAD\u4ea4BE\u4e8eH\uff0c\u4e14BH=AC\uff0c\u6c42\u2220ABC\u3002
3\u5df2\u77e5\u2220AOB\uff0cP\u4e3a\u89d2\u5e73\u5206\u7ebf\u4e0a\u4e00\u70b9\uff0cPC\u22a5OA\u4e8eC\uff0c\u2220OAP+\u2220OBP=180\u00b0\uff0c\u6c42\u8bc1\uff1aAO+BO=2CO\u3002
4\u5df2\u77e5\u0394ABC\u662f\u76f4\u89d2\u4e09\u89d2\u5f62\uff0cAB=AC\uff0cM\u662fAC\u4e2d\u70b9\uff0cAD\u22a5BM\u4e8eD\uff0c\u5ef6\u957fAD\u4ea4BC\u4e8eE\uff0c\u8fde\u63a5EM\uff0c\u6c42\u8bc1\uff1a\u2220AMB=\u2220EMC\u3002
5\u5df2\u77e5\u0394ABC\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cDE\u22a5AB\u4e8eE\uff0cDF\u22a5AC\u4e8eF\uff0c\u6c42\u8bc1\uff1aAD\u22a5EF\u3002
6\u5df2\u77e5\u0394ABC\uff0c\u2220B=90\u00b0\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cDE\u22a5AC\u4e8eE\uff0cF\u5728AB\u4e0a\uff0cBF=CE\uff0c\u6c42\u8bc1\uff1aDF=DC\u3002
7\u5df2\u77e5\u0394ABC\uff0c\u2220A\u4e0e\u2220C\u7684\u5916\u89d2\u5e73\u5206\u7ebf\u4ea4\u4e8eP\uff0c\u8fde\u63a5PB\uff0c\u6c42\u8bc1\uff1aPB\u5e73\u5206\u2220B\u3002
8\u5df2\u77e5\u0394ABC\uff0c\u5230\u4e09\u8fb9AB\uff0cBC\uff0cCA\u7684\u8ddd\u79bb\u76f8\u7b49\u7684\u70b9\u6709\u51e0\u4e2a\uff1f
9\u5df2\u77e5\u56db\u8fb9\u5f62ABCD\uff0cAD\u2016BC\uff0cAD\u22a5DC\uff0cE\u4e3aCD\u4e2d\u70b9\uff0c\u8fde\u63a5AE\uff0cAE\u5e73\u5206\u2220BAD\uff0c\u6c42\u8bc1\uff1aAD+BC=AB\u3002
10\u5df2\u77e5\u0394ABC\uff0cAD\u662f\u89d2\u5e73\u5206\u7ebf\uff0cBE\u22a5AD\u4e8eE\uff0c\u8fc7E\u4f5cAC\u7684\u5e73\u884c\u7ebf\uff0c\u4ea4AB\u4e8eF\uff0c\u6c42\u8bc1\uff1a\u2220FBE=\u2220FEB\u3002
(1)\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62
\u8bc1\u660e;\u8fde\u63a5AD\uff0c\u56e0\u2220BAC=90\u00b0\uff0cAB=AC\uff0cD\u4e3aBC\u4e2d\u70b9\uff0c
\u53ef\u77e5\uff1aAD=BD=CD\u3001\u2220ADB=90\u00b0\uff0c\u53ef\u77e5\u2220CAD=\u2220ABC=45\u00b0\uff0c\u53c8\u56e0AN=BM\uff0c
\u5219\u25b3ADN\u224c\u25b3BDM\uff0c\u56e0\u6b64DN=DM\u3001\u2220ADN=\u2220BDM\uff0c\u5f97\u2220MDN=90\u00b0
\uff082\uff09\u6839\u636e\u4f60\u7684\u6761\u4ef6\uff0c\u6240\u6c42\u9762\u79ef\u4e0d\u662f\u5b9a\u503c\u572814\u548c28\u4e4b\u95f4
所以D为AC的中点,即AD=CD=AC/2
所以(1)当AB=AC>BC时,有AB+AD=3AD=30, BC+CD=24
AD=10=CD
所以AB=AC=20, BC=24-CD=24-10=14
此时三角形三边长为20,20,14,经检验,三边能构成三角形,结果成立
(2)当AB=AC<BC时,有AB+AD=3AD=24, BC+CD=30
AD=8=CD
所以AB=AC=16, BC=30-CD=30-8=22
此时三角形三边长为16,16,22, 经检验,三边能构成三角形,结果成立
综上所述,三角形三边长分别为20,20,14或16,16,22
中线BD把三角形分成了两部分。设腰长等于x，底长等于y。根据题意知道2x+y=24+30=54
一部分是半个腰长与一个腰长，即AB+AD.=3x/2
另一部分是半个腰长与一个底长,即BC+CD.=x/2+y
如果AB+AD=24 即 3x/2=24 那么 x=16 y=22
如果AB+AD=30 即 3x/2=30 那么x=20 y=14
所以 三条边可以是16、16、22 或者 20、20、14.
解：设AB=AC=X，BC=Y;
根据题目意思，有两种情况：AD+AB=24，BC+CD=30或者AD+AB=24，BC+CD=30
1）当第一种情况下 AD+AB=24，BC+CD=30：
也就是1.5X=24则X=16(因为AD=0.5X,AB=X)
Y+0.5X=30，则Y=22
2) 当第二种情况下 AD+AB=30，BC+CD=24：
也就是1.5X=30，则X=20
Y+0.5X=24，则Y=14
所以，这样子的三角形有两种情况：AB=AC=16，BC=22或者AB=AC=20，BC=14
设AB=AC=a,BC=b
则根据题意可得，
分两种情况，
1.
AB+AD=a+a/2=24
BC+CD=b+a/2=30
可得a=16,b=22
则三角形三边长为16，16，22
2.
AB+AD=a+a/2=30
BC+CD=b+a/2=24
可得
a=20,b=14
则三角形三边长为20，20，14
设三角形的腰为x
1°x + 2/x = 24
x=16
所以三角形的周长为24+30=54cm
三边长分别为 16 ，16，22
2°x + 2/x = 30
x=20
三角形的周长为24+30=54cm
三边长分别为 20 ，20 ，14
绛旓細鎵浠B=AC=16, BC=30-CD=30-8=22 姝ゆ椂涓夎褰涓夎竟闀夸负16,16,22, 缁忔楠,涓夎竟鑳芥瀯鎴愪笁瑙掑舰,缁撴灉鎴愮珛 缁间笂鎵杩,涓夎褰笁杈归暱鍒嗗埆涓20,20,14鎴16,16,22
绛旓細杩嘊鍋欱Q鍨傜洿浜嶢C銆傚彲寰楋細S涓夎褰ABC=1/2*AB*BC=1/2AC*BQ銆傛墍浠1/2*8*6=1/2*10*BQ锛岃В寰桞Q=4.8銆傛墍浠C杈逛笂鐨勯珮鏄4.8銆傝繃P鍋歅M鍨傜洿浜嶢B銆備笁瑙掑舰AMP鐩镐技浜庝笁瑙掑舰ABC锛屾墍浠P/PM=AC/BC锛屾墍浠10-X/PM=AC/BC PM=6-3/5X銆俌=1/2AB*PM=1/2*8*锛6-3/5X锛=24-12/5X銆傛墍...
绛旓細1銆佷綔AH鈯C锛屽垯BH=AB*cosB=c*cosB,(1)CH=AC*cosC=b*cosC,(2)(1)+(2),c*cosB+b*cosC=BH+CH=BC=a,宸茬煡锛宐*cosC=2a*cosB-c*cosB,b*cosC+c*cosB=a=2a*cosB,cosB=1/2,鈭碆=60掳銆2銆丼鈻矨BC=AH*BC/2=AH*4/2=5鈭3锛孉H=5鈭3/2锛孉H/BH=tanB=tan60掳=鈭3锛孊H=锛5鈭...
绛旓細3x+2x+3x=56 瑙ｅ緱 x=7 鈭翠笁杈归暱鍒嗗埆鏄21銆21銆14 鈶¤涓夎竟闀垮垎鍒槸2x銆2x銆3x锛屽垯 2x+2x+3x=56 瑙ｅ緱 x=8 鈭翠笁杈归暱鍒嗗埆鏄16銆16銆24
绛旓細1.鏄紝鍥犱负AB=AC,BD=DC,瑙払=瑙扖,鎵浠涓夎褰ABD鍏ㄧ瓑浜嶢CD,鎵浠ヨADB=ADC=90掳 2鍥犱负,EO=FO锛孊O=DO锛屾墍浠E=DF鍙圓B=CD,AE=CF鎵浠ヤ笁瑙掑舰ABE鍏ㄧ瓑浜嶤DF锛屾墍浠ワ細鈭燘=鈭燚銆3.鍥犱负ABECFB=DE,AF=DC,鈭燗=鈭燚鎵浠ヤ笁瑙掑舰ABF鍏ㄧ瓑浜嶤DE锛屾墍浠F=CE鍙,BC=EF鎵浠CEF鏄钩琛屽洓杈瑰舰锛屾墍浠C涓嶦F骞宠...
绛旓細浣淏E鍨傜洿浜嶢D浜嶦 锛屽垯 BA锛10鈭2 BE锛滵E锛滲A 梅2锛10鈭2 梅2锛5鈭2 AE锛濃垰锛圓B² - BE²锛夛紳鈭氾紙锛10鈭2锛² - 锛5鈭2锛²锛夛紳鈭氾紙200 - 50锛夛紳5鈭6 AD锛滱E+DE锛5鈭6 + 5鈭2 涓夎褰ABD鐨勯潰绉槸锛氾紙5鈭6 + 5鈭2锛壝楋紙5鈭2锛壝2 锛濓紙50鈭...
绛旓細瑙1S螖ABE=1/2S螖ABC=1/2脳1/2脳AB脳AC=1/2脳1/2脳8脳6=12 2涓夎褰ABE鍜屼笁瑙掑舰ACE鐨勫懆闀垮樊 =AB-AC =8-6 =2
绛旓細绛旀 銆愮瓟妗堛戝垎鏋愶細鐢遍鎰忓緱锛氣垹A=30掳锛屸垹FDE=45掳锛屽埄鐢ㄥ钩瑙掔瓑浜180掳锛屽彲寰楀埌鈭燗DF鐨勫害鏁帮紝鍦ㄢ柍AMD涓紝鍒╃敤涓夎褰鍐呰鍜屼负180掳锛屽彲浠ユ眰鍑衡垹AMD鐨勫害鏁帮紟瑙ｇ瓟锛氳В锛氣埖鈭燘=60掳锛屸埓鈭燗=30掳锛屸埖鈭燘DE=70掳锛屸垹FDA=45掳锛屸埓鈭燗DF=180掳-70掳-45掳=65掳锛屸埓鈭燗MD=180掳-30...
绛旓細鐪嬫潵妤间富娌″杩"浣欏鸡瀹氱悊",鎹釜鍒濈骇鐨勮В娉曞涓:瑙:璁锯娍ABC涓,AB=AC=1,鈭燘AC=135掳.浣淏D鍨傜洿CA鐨勫欢闀跨嚎浜嶥,鍒:鈭燘AD=180掳-鈭燘AC=45掳.鈭碆D=AD=(鈭2/2)AB=鈭2/2,CD=AC+AD=1+鈭2/2.鈭碆C=鈭(CD²+BD²)=鈭歔(1+鈭2/2)²+(鈭2/2)²]=鈭(2+鈭2)...
绛旓細瑙ｏ細鍥犱负 DE锛孧N鍒嗗埆鏄疉B锛孉C鐨勫瀭鐩村钩鍒嗙嚎锛屾墍浠 AE=BE锛孉N=CN锛屾墍浠 瑙払AE=瑙払锛 瑙扖AN=瑙扖锛屽洜涓 瑙払AC+瑙払+瑙扖=180搴︼紝瑙払AC=a,锛屾墍浠 瑙払+瑙扖=180搴--a 鍥犱负 瑙払AE=瑙払锛岃CAN=瑙扖锛屾墍浠 瑙払AE+瑙扖AN=瑙払+瑙扖=180搴--a锛屽嵆 瑙払AC+瑙扙AN=180...
