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:
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