如图,在△ABC中,BA=BC,D在边CB上,且DB=DA=AC.(1)如图1,填空∠B= 如图,在Rt△ABC中,∠ACB=90°,AC=6,BC=8...

\u5982\u56fe\uff0c\u5728\u25b3ABC\u4e2d\uff0cBA=BC\uff0cD\u5728\u8fb9CB\u4e0a\uff0c\u4e14DB=DA=AC\uff0e\uff081\uff09\u5982\u56fe1\uff0c\u2220B=______\uff1b\u2220C=______\uff0e\uff082\uff09\u5982\u56fe2\uff0cM\u4e3a

\uff081\uff09\u2235DB=DA\uff0c\u2234\u2220B=\u2220BAD\uff0c\u2234DA=AC\uff0c\u2234\u2220C=\u2220ADC\uff0c\u2235BA=BC\uff0c\u2234\u2220C=\u2220BAC\uff0c\u5728\u25b3ABD\u4e2d\uff0c\u2220ADC=\u2220B+\u2220BAD=2\u2220B\uff0c\u2234\u2220C=\u2220BAC=2\u2220B\uff0c\u5728\u25b3ABC\u4e2d\uff0c\u2220BAC+\u2220B+\u2220C=180\u00b0\uff0c\u53732\u2220B+\u2220B+2\u2220B=180\u00b0\uff0c\u89e3\u5f97\u2220B=36\u00b0\uff0c\u2234\u2220C=2\u2220B=2\u00d736\u00b0=72\u00b0\uff1b\uff082\uff09CD=BN+CE\uff0e\u7406\u7531\u5982\u4e0b\uff1a\u5728\u25b3ACD\u4e2d\uff0c\u2220CAD=180\u00b0-72\u00b0\u00d72=36\u00b0\uff0c\u2235\u2220B=\u2220BAD=36\u00b0\uff0c\u2234\u2220BAD=\u2220CAD\uff0c\u2235MH\u22a5AD\uff0c\u2234\u2220AHN=\u2220AHE=90\u00b0\uff0c\u2235\u5728\u25b3ANH\u548c\u25b3AEH\u4e2d\uff0c\u2220BAD\uff1d\u2220CADAH\uff1dAH\u2220AHN\uff1d\u2220AHE\uff1d90\u00b0\uff0c\u2234\u25b3ANH\u224c\u25b3AEH\uff08ASA\uff09\uff0c\u2234AN=AE\uff0c\u53c8\u2235AB=BC\uff0c\u2234BN=AB-AN=BC-AE\uff0c\u7531\u56fe\u53ef\u77e5\uff0cCE=AE-AC\uff0c\u53c8\u2235CD=BC-BD=BC-AD=BC-AC\uff0c\u2234CD=BN+CE\uff1b\uff083\uff09\u5982\u56fe\uff0cM\u4e3aBC\u7684\u4e2d\u70b9\u65f6\uff0cBM=CM\uff0c\u8fc7\u70b9C\u4f5cCF\u2225AB\u4ea4NE\u4e8eF\uff0c\u5219\u2220B=\u2220MCF\uff0c\u2220ANE=\u2220CFE\uff0c\u2235\u5728\u25b3BMN\u548c\u25b3CMF\u4e2d\uff0c\u2220B\uff1d\u2220MCFBM\uff1dCM\u2220BMN\uff1d\u2220CME\uff0c\u2234\u25b3BMN\u224c\u25b3CMF\uff08ASA\uff09\uff0c\u2234BN=CF\uff0c\u7531\uff082\uff09\u53ef\u77e5\u25b3ANH\u224c\u25b3AEH\uff0c\u2234\u2220ANE=\u2220E\uff0c\u2234\u2220CFE=\u2220E\uff0c\u2234CE=CF\uff0c\u5728\uff082\uff09\u7684\u6761\u4ef6\u4e0b\uff0cCD=BN+CE=CF+CE=CE+CE=2CE\uff0c\u2234CDCE=2\uff0e\u6545\u7b54\u6848\u4e3a\uff1a2\uff0e

\u60c5\u51b5\u4e00\uff0cAC=AB`=6,\u5219BB`=4,\u56e0\u4e3a\u5bf9\u79f0\uff0c\u6240\u4ee5BE=2,\u56e0\u4e3a\u76f8\u4f3c\u4e09\u89d2\u5f62,∆BDE\u76f8\u4f3c\u4e8e∆ABC\uff0c\u6240\u4ee5BD/BE=BA/BC,BD=2.5
\u60c5\u51b5\u4e8cCA=CB`=6,\u5219\u8fc7C\u4f5cCF\u5782\u76f4AB\u4e8eF,\u6240\u4ee5∆ACF\u76f8\u4f3c\u4e8e∆ABC,\u6240\u4ee5\uff0cAC/AF=AB/AC,\u6240\u4ee5AF=3.6,\u6240\u4ee5\uff0cAB`=7.2,\u63a5\u4e0b\u6765\uff0c\u6b65\u9aa4\u540c\u60c5\u51b5\u4e00\uff0c\u53ef\u5f97BD=3.5
\u60c5\u51b5\u4e09\uff0cAB`=AC`\uff0c\u7531\u4e2d\u4f4d\u7ebf\u53ef\u77e5\uff0cB`\u4e3aAB\u4e2d\u70b9\uff0c\u6240\u4ee5BB`=5,\u63a5\u4e0b\u6765\u6b65\u9aa4\u540c\u60c5\u51b5\u4e00\uff0c\u53ef\u5f97BD=😄3.125
\u60c5\u51b5\u56db\uff0c∆ACB`\u4e3a\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u4e0d\u53ef\u80fd\u6210\u7acb

(1)∵BA=BC,
∴∠BCA=∠BAC,
∵DA=DB,
∴∠BAD=∠B,
∵AD=AC,
∴∠ADC=∠C=∠BAC=2∠B,
∴∠DAC=∠B,
∵∠DAC+∠ADC+∠C=180°,
∴2∠B+2∠B+∠B=180°,
∴∠B=36°,∠C=2∠B=72°,
故答案为:36;72;
(2)①在△ADB中,∵DB=DA,∠B=36°,
∴∠BAD=36°,
在△ACD中,∵AD=AC,
∴∠ACD=∠ADC=72°,
∴∠CAD=36°,
∴∠BAD=∠CAD=36°,
∵MH⊥AD,
∴∠AHN=∠AHE=90°,
∴∠AEN=∠ANE=54°,
即△ANE是等腰三角形;
②CD=BN+CE.
证明:由①知AN=AE,
又∵BA=BC,DB=AC,
∴BN=AB-AN=BC-AE,CE=AE-AC=AE-BD,
∴BN+CE=BC-BD=CD,
即CD=BN+CE.

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