2022年中考题中与三角形有关的综合题 .pdf

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1、中考题中与三角形有关的综合题类型一：构造法添加辅助线1如图 1，已知 BD平分 ABC，AC=BC，C=90，AE BD于 E，判断 AE与 BD的数量关系并证明.图 1 2如图 3，在 ABC中，BAC=90，AB=AC，D为 AC的中点，AEBD于 E，延长 AE交 BC于 F，求证：ADB=CDF 图 3 类型二：在变化的图中探究同一类问题这类问题往往是方法的延续，而第一问是很容易入手的，因此对比第一问，利用第一问的方法就可以解决后面的问题1.如图 6，点 O是线段 AD的中点，分别以 AO和 DO为边在线段 AD的同侧作等边三角形OAB 和等边三角形 OCD，连结 AC和 BD，相交于

2、点 E，连结 BC 求 AEB的大小；（2）如图 8，OAB 固定不动，保持 OCD 的形状和大小不变，将 OCD绕着点 O旋转（OAB 和 OCD 不能重叠），求 AEB的大小.文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:

3、CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 H

4、K7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX

5、10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编

6、码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6

7、 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9

8、ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2思路点拨：题中 BD 平分ABC，且 BDAE，由此可以构造等腰三角形延长 AE，与

9、 BC 延长线交于点O.易证 ABE OBE，可知 ABO 是等腰三角形，AO=2AE，而可证 AOC BDC，知AO=BD，进而知道 BD=2AE 文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7

10、Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10

11、M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:

12、CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 H

13、K7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX

14、10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编

15、码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2图 2 解析：BD=2AE，证明如下：延长 AE，与 BC延长线交于点O，如图 2 BD平分 ABC，2=3.AE

16、 BD于 E，AEB=OEB=90.在 ABE和 OBE中，ABE OBE（ASA）AE=OE，AO=2AE.C=90 ACO=BCD=90，1+O=90 2+O=90，1=2 在 AOC和 BDC中 AOC BDC（ASA）AO=BD BD=2AE.总结升华：这种构造方法是一种常见的添加辅助线的方法思路点拨：（1）ADB 与 CDF 这两个角不在任一对全等三角形中，因此直接证很困难，我们可以考虑构造全等三角形，而且这两个三角形要含有ADB 和 CDF 在 CDF 中，C=45,因此另一个三角形中必含有 45 角过 A 作 AO BC 于 O，与 BD 交于点 M，易证 ABM CAF，AM=

17、CF，接下来只须证AMD CFD 即可（2）我们也可以将角进行转换，由已知AB=AC 分析，可过C 作 CGAC 交 AF延长线于 G，就可以构造文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6

18、O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9

19、M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL

20、2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7

21、Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10

22、M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:

23、CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2ACG BAD，ADB=G，接下来只需证CDF CGF，得 G=CDF 即可解析：（法一）过A作 AO BC于 O，与

24、 BD交于点 M，如图 4 2+BAE=90，3+BAE=90 2=3 1=C=45，AB=AC 在 ABM 和 CAF中 ABM CAF(ASA)图 4 AM=CF MAD=C=45，AD=CD 在 AMD 和 CFD中 AMD CFD(SAS)ADB=CDF.（法二）过C 作 CGAC 交 AF 延长线于G，如图 5 ACG=BAD=90 2+1=90，3+1=90 2=3 在 ACG 和 BAD 中，ACG BAD（ASA）G=ADB，CG=AD 图5D 为 AC 中点，AD=CD，CG=CD BAC=90 ，AB=AC，ACG=90 FCG=DCF=45 在 CDF 和 CGF 中文档

25、编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X

26、6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9

27、 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2

28、文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M

29、5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5

30、B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4

31、O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2 CDF CGF（SAS）G=CDF，ADB=CDF.总结升华：当题目中的结论在现有图形中难以解决时，我们自然会考虑添加辅助线，而构造全等三角形来转化线段或角是我们常用的方法之一思路点拨：（1）中的求解方法很多，但考虑到与（2）的联系，就需要有很强的识图能力，而题目中

32、已知的角只有60，因此应该让AEB与之建立联系观察到图中含有“8”字形图，如右图，A+O=E+B，而由已知易证AOC BOD，OAC=OBD，因此 AEB=AOB=60 解析：（1）在等边三角形OAB和等边三角形OCD 中，OC=OD，OA=OB，AOB=COD=60，AOB+BOC=COD+BOC，即 AOC=BOD 在 AOC 和 BOD中 AOC BOD（SAS）OAC=OBD 1=OAC+AOB=OBD+AEB AEB=AOB=60 （2）同（1）可证AEB=AOB=60 总结升华：（1）解决这类问题应该统筹考虑这两问，从而得到最佳解题方案从解题思路可知，记住一些基本图形很有必要除了“

33、8”字形图之外，还需记住“燕尾形”图，如图9，D=A+文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B

34、9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O

35、2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1

36、M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U

37、5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V

38、4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7

39、W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2B+C（2）本题中 OA与 OD不相等，结论依然成立，留给同学们字形解决（2）同（1）可证 AEB=AOB=60 图 9 文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编

40、码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6

41、 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9

42、ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文

43、档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5

44、X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B

45、9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2文档编码:CL2V7W1M5X6 HK7Y6O1U5B9 ZX10M9M2V4O2