类比、转化、从特殊到一般等思想方法,在数学学习和研究中经常用到,如下是一个案例,请补充完整.
原题:如图1,在平行四边形
中,点
是
的中点,点
是线段
上一点,
的延长线交射线
于点
.若
,求
的值.
![](https://img.xkw.com/dksih/QBM/2020/11/19/2596340784128000/2601452338790400/STEM/17134864-40b2-4f3d-8025-cc02c939326a.png?resizew=578)
(1)尝试探究
在图1中,过点
作
交
于点
,则
和
的数量关系是_________,
和
的数量关系是_________,
的值是_________.
(2)类比延伸
如图2,在原题的条件下,若
,则
的值是_________(用含有
的代数式表示),试写出解答过程.
(3)拓展迁移
如图3,梯形
中,
,点
是
的延长线上的一点,
和
相交于点
.若
,
,
,则
的值是________(用含
、
的代数式表示).
原题:如图1,在平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8017580f716b548c192e72e04e1ccad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803c907aa8d31a9359f24405990fc92.png)
![](https://img.xkw.com/dksih/QBM/2020/11/19/2596340784128000/2601452338790400/STEM/17134864-40b2-4f3d-8025-cc02c939326a.png?resizew=578)
(1)尝试探究
在图1中,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb50903843f7b423084a954e46adeb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589786dd7c3a2679c3230b671cd232d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803c907aa8d31a9359f24405990fc92.png)
(2)类比延伸
如图2,在原题的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea82411d04daefd2d45906278b24f4e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803c907aa8d31a9359f24405990fc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)拓展迁移
如图3,梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bdb3995265a321989202ff01001013d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89309239f6bcaf4d978030b6768d72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c3ee47f8df069c96bc61c7ec32b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f311053d11884b1a21d5f9b5724996c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec395fe7a4bc51dac28c37085fabcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
2019九年级·全国·专题练习 查看更多[10]
专题二 猜想证明类例题湖南省永州市新田县2019-2020学年九年级上学期期中数学试题2020年湖南省长沙市长郡滨江中学中考数学3月模拟试题(已下线)【万唯原创】2015年河南省中考数学2014年真题-2012年河南省初中学业水平暨高级中等学校(已下线)【万唯原创】2016年河南省中考数学-2015年真题-2012年河南省初中学业水平暨高级中等学校招生考试山东省鄄城县2020-2021学年九年级上学期期中数学试题(已下线)类型二 与线段有关的问题-2021年《三步冲刺中考·数学》(陕西专用)之第2步大题夺高分山西省太原市第五中学2021-2022学年九年级上学期阶段考试数学试题山西省太原市第五中学校2021-2022学年九年级上学期10月月考数学试题河南省驻马店市第二初级中学2021-2022学年九年级上学期期末数学试题
更新时间:2020-11-26 20:51:14
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【知识点】 相似三角形的判定与性质综合
相似题推荐
解答题-证明题
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【推荐1】在正方形
中,点G是边
上的一个动点,点
在边
上,
,且
,
的延长线相交于点P.
(1)如图1,当点E与点C重合时,求
的度数;
(2)如图2,当点E与点C不重合时,问:(1)中
的度数是否发生变化,若有改变,请求出
的度数,若不变,请说明理由;
(3)在(2)的条件下,作
于点N,连接
,取
的中点M,连接
,在点G的运动过程中,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5842cd648ff2c62e66b2dd1c1ee3863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcfc97319d4d6ae2f362586cc9108e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be109148d3340814f0149bbddd85586a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c3ab516557c398dc7ed3962e5a2555.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/e705290e-ac49-4e6c-a8e1-fcdedb1ee6d6.png?resizew=490)
(1)如图1,当点E与点C重合时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19768d8c55deb4973820aeab7a224e6a.png)
(2)如图2,当点E与点C不重合时,问:(1)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19768d8c55deb4973820aeab7a224e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19768d8c55deb4973820aeab7a224e6a.png)
(3)在(2)的条件下,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d28afeda2e33b875e9e4c27760c4a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f52f30b6ef12b5d6a5b9decde17160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ba34242cd639f1446a2999ecf78ba8.png)
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解答题-证明题
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【推荐2】如图,已知⊙Q的半径为2,在⊙Q的对称轴l1上取一点O,使得OQ=
(点O在点Q的下方),过O作直线l2⊥l1,P为直线l2上的一点,过点P作⊙Q的切线PA,PB,切点为A,B,连接AB.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986243852902400/2990579795238912/STEM/4e987582-c417-4170-aba8-8aa6f8b96389.png?resizew=302)
(1)当OP=OQ时,求PA的长;
(2)连接PQ,当PQ⋅AB最小时,求PA的长;
(3)试证明点P在直线l2上运动时,弦AB必经过一个定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30efdb9c7eb4b788352056f3edf21635.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986243852902400/2990579795238912/STEM/4e987582-c417-4170-aba8-8aa6f8b96389.png?resizew=302)
(1)当OP=OQ时,求PA的长;
(2)连接PQ,当PQ⋅AB最小时,求PA的长;
(3)试证明点P在直线l2上运动时,弦AB必经过一个定点.
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【推荐3】在
ABC和
DEC中,∠ACB=∠DCE=90°,BC=AC,EC=DC
![](https://img.xkw.com/dksih/QBM/2022/4/9/2954378119684096/2955950361960448/STEM/5f055102-0f12-45e1-85ec-5cefb7724422.png?resizew=595)
(1)当点D,F重合时,则AF,BF,CF之间的数量关系为 ;
(2)如图(2),点E在
ABC内部,直线AD与BE交于点F.当点D,F不重合时,证明(1)中的结论仍然成立.
(3)如图(3),在
ABC和
DEC中,∠ACB=∠DCE=90°,BC=kAC,EC=kDC(k是常数),点E在
ABC内部,直线AD与BE交于点F.则线段AF,BF,CF之间满足什么数量关系,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/2022/4/9/2954378119684096/2955950361960448/STEM/5f055102-0f12-45e1-85ec-5cefb7724422.png?resizew=595)
(1)当点D,F重合时,则AF,BF,CF之间的数量关系为 ;
(2)如图(2),点E在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(3)如图(3),在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
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