摘要：26． (1)如图1.图2.图3.在中.分别以为边.向外作正三角形.正四边形.正五边形.相交于点． ①如图1.求证:, ②探究:如图1. , 如图2. , 如图3. ． (2)如图4.已知:是以为边向外所作正边形的一组邻边,是以为边向外所作正边形的一组邻边．的延长相交于点． ①猜想:如图4. (用含的式子表示), ②根据图4证明你的猜想． (1)①证法一:与均为等边三角形. .························································································ 2分 且··············································· 3分 . 即························································ 4分 ．··················································· 5分 证法二:与均为等边三角形. .························································································ 2分 且························································································ 3分 可由绕着点按顺时针方向旋转得到··································· 4分 ．··························································································· 5分 ②..．········································································ 8分 (2)①········································································································ 10分 ②证法一:依题意.知和都是正边形的内角... .即．····························· 11分 ．·························································································· 12分 ..······ 13分 . ········································ 14分 证法二:同上可证 ．··························································· 12分 .如图.延长交于. . ································ 13分 ················· 14分 证法三:同上可证 ．··························································· 12分 ． . ························································ 13分 即········································································ 14分 证法四:同上可证 ．··························································· 12分 ．如图.连接. ．···································· 13分 即······························· 14分 注意:此题还有其它证法.可相应评分．

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