【问题呈现】
和
都是直角三角形,
,
,
,连接
、
,探究
、
的位置关系.
【问题探究】
(1)如图①,当
时,判断
、
的位置关系,并说明理由.
(2)如图②,当
时,
、
的位置关系为______.
【拓展应用】
(3)当
,
,
时,将
绕点C旋转、使A,D,E三点恰好在同一直线上,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41663d9e5e18891475aeaa98794f33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99100a3ec33eecf804076f76c905359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818e07559cd9ec3810dcb4d0cdb6a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
【问题探究】
(1)如图①,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
(2)如图②,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
【拓展应用】
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4590b1db8451f30e1021e68b8359c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a88770433e9897d78d28ccfaab8b506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/617a843d-cc61-479e-b34a-9ea7cac75f7f.png?resizew=791)
更新时间:2024-03-06 16:20:52
|
相似题推荐
解答题-证明题
|
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【推荐1】如图,在边长为
的正方形ABCD中,作∠ACD的平分线交AD于F,过F作直线AC的垂线交AC于P,交CD的延长线于Q,又过P作AD的平行线与直线CF交于点E,连接DE,AE,PD,PB.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/25ec4821-e57b-4d3c-bca8-c3a4e9ce4b2e.png?resizew=194)
(1)求AC,DQ的长;
(2)四边形DFPE是菱形吗?为什么?
(3)探究线段DQ,DP,EF之间的数量关系,并证明探究结论;
(4)探究线段PB与AE之间的数量关系与位置关系,并证明探究结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/13/25ec4821-e57b-4d3c-bca8-c3a4e9ce4b2e.png?resizew=194)
(1)求AC,DQ的长;
(2)四边形DFPE是菱形吗?为什么?
(3)探究线段DQ,DP,EF之间的数量关系,并证明探究结论;
(4)探究线段PB与AE之间的数量关系与位置关系,并证明探究结论.
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【推荐2】探究题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/073b82d8-00c9-497c-ab8a-41172b5a3dcf.png?resizew=500)
(1)如图1,△ACB和△DCE均为等边三角形,点A,D,E在同一直线上,连接BE,则
的度数为______;线段AD,BE之间的数量关系为______;
(2)如图2,△ACB和△DCE均为等腰三角形,
,点A,D,E在同一直线上,CM为△DCE中DE边上的高,连接BE,请猜测
的度数及线段CM,AE,BE之间的数量关系,并说明理由.
(3)如图3,在正方形ABCD中,
,若点P满足
,且
,请直接写出点A到BP的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/073b82d8-00c9-497c-ab8a-41172b5a3dcf.png?resizew=500)
(1)如图1,△ACB和△DCE均为等边三角形,点A,D,E在同一直线上,连接BE,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a55a1a244f81097e05e715b69580faa.png)
(2)如图2,△ACB和△DCE均为等腰三角形,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc75953bf5dcfa4af308c34bf9952d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a55a1a244f81097e05e715b69580faa.png)
(3)如图3,在正方形ABCD中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d5974e8669eb588401203de18a3ff7.png)
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【推荐3】综合与实践课上,老师给出定义:对角线互相垂直的四边形叫做“垂美四边形”.同学们以此开展了数学活动.
,使得
,
,那么四边形
______“垂美四边形”.(填“是”或“不是”)
②如图2,分别以
的直角边
和斜边
为边向外作正方形
和正方形
,连接
、
、
.那么四边形
是“垂美四边形”吗?请说明理由.
拓展探究
(2)如图3,四边形
是“垂美四边形”,则两组对边
与
之间有什么数量关系?请说明理由.
迁移应用
(3)如图4,在
中,
,
,
.
分别是射线
,
上一个动点,同时从点
出发,分别沿
和
方向以每秒5个单位长度和每秒21个单位长度的速度匀速运动,运动时间为
秒,连接
与
交于点
,当以点
,
,
,
为顶点的四边形是“垂美四边形”时,直接写出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4009aa13093cc3865dcd51b371892160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
②如图2,分别以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76899b3a0bfbbdae7cb1148ad4bf018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7a0bfc593a8a33b6cade6ba213904c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f3956f008cc29ca4bae44a087d5427.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693cd6179b2a92f03153ce12a0e86b95.png)
拓展探究
(2)如图3,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6c8b21a087818284c9cd909cc56c814.png)
迁移应用
(3)如图4,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a30b304391aa7133499fc535bd9e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解答题-问答题
|
较难
(0.4)
名校
【推荐1】如图,在
中,
,
,
,D是边
上一点(两端点除外),经过D,C,E三点的
交
于点A,连接
,点B是
上一点.且满足
,连接
,
,分别交EF于点H,G.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/6fe60fa6-9af7-4891-a3fe-695894debdb8.png?resizew=126)
(1)求证:
;
(2)若
.
①求
的半径;
②求
的长;
(3)求线段
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc301e70210440383c644899d2fc4f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e03081d213f86214c680dbd91118ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f7d9f5e71bfef8188b1216c1276c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cec73fce3ed065803d763c700124a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f986c181183d8e7e45655e6c5b5d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb27272b4eb9ed057dd3b4d40697e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/6fe60fa6-9af7-4891-a3fe-695894debdb8.png?resizew=126)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d278a57ac867399c2da09177202260.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
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【推荐2】对于面积为S的三角形和直线l,将该三角形沿直线l折叠,重合部分的图形面积记为
,定义
为该三角形关于直线l的对称度.如图,将面积为S的
ABC沿直线l折叠,重合部分的图形为
,将
的面积记为
,则称
为
ABC关于直线l的对称度.
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893464109498368/2895882938580992/STEM/ed52df7a-aa75-4f1c-8a96-6c82d49f96f4.png?resizew=210)
在平面直角坐标系xOy中,点A(0,3),B(-3,0),C(3,0).
(1)过点M(m,0)作垂直于x轴的直线
,
①当
时,
ABC关于直线
的对称度的值是 :
②若
ABC关于直线
的对称度为1,则m的值是 .
(2)过点N(0,n)作垂直于y轴的直线
,求△ABC关于直线
的对称度的最大值.
(3)点P(-4,0)满足
,点Q的坐标为(t,0),若存在直线,使得
APQ关于该直线的对称度为1,写出所有满足题意的整数t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e9a64b5a082ec9e87bcc67e6afa1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e807ed5636b783c51603d38337313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e807ed5636b783c51603d38337313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f562eb3c2a45d65cba066d712825a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e9a64b5a082ec9e87bcc67e6afa1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893464109498368/2895882938580992/STEM/ed52df7a-aa75-4f1c-8a96-6c82d49f96f4.png?resizew=210)
在平面直角坐标系xOy中,点A(0,3),B(-3,0),C(3,0).
(1)过点M(m,0)作垂直于x轴的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)过点N(0,n)作垂直于y轴的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)点P(-4,0)满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574dc284fb9e74d65cf0c79a978d65de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
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解答题-证明题
|
较难
(0.4)
【推荐1】如图,在
中,点
,
分别在
,
上,且
.
(1)【问题背景】如图1,若
,求证:
;
(2)已知
,
.
①【变式运用】如图2,若
,
,求证:
;
②【拓展创新】如图3,若
,
,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102e836344156ea835d7d4e9b4120fe8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/9/8d221519-9fec-45ab-ba8a-450407660fac.png?resizew=632)
(1)【问题背景】如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4354365ca0929f8a606ed0bf341e4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6266143305e09d19f818844ec3720970.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df049f15adb6667113ceee3a6638cd0a.png)
①【变式运用】如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb08f6a798dc293f3d8de281190f65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8df4cab7eba6ec0757ed086af7c7741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d00f4651b343dd8f9060c6460f0c955.png)
②【拓展创新】如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d00f4651b343dd8f9060c6460f0c955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d755163f217efac832d87eb2c41cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
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解答题-作图题
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【推荐2】如图,在
中,点
在边
上,且
,已知
,
.
(1)求
的度数;
(2)我们把有一个内角等于
的等腰三角形称为黄金三角形.它的腰长与底边长的比(或者底边长与腰长的比)等于黄金比
.
①写出图中所有的黄金三角形,选一个说明理由;
②求
的长;
③在直线
或
上是否存在点
(点
、
除外),使
是黄金三角形?若存在,在备用图中画出点
,简要说明画出点
的方法(不要求证明);若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fa696c52ea83507b14ae85b37a2fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad7f8fa5f627ec55400a3cadd912801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f976007b8d754ac3bf5793ed2fce37.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f693e870d5ccdced6e023cc4f7d621.png)
(2)我们把有一个内角等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6b14146fe92c0d8216e32926ad4371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ac144ea34a0a5abced9ea7736f37ec.png)
①写出图中所有的黄金三角形,选一个说明理由;
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
③在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9017cfed5393f9b21602107ed164c733.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2018/12/21/2101758422433792/2104556894715904/STEM/a0e4c6a1bff54200a9ad6bee72612327.png?resizew=213)
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解答题-证明题
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真题
【推荐3】根据相似多边形的定义,我们把四个角分别相等,四条边成比例的两个凸四边形叫做相似四边形.相似四边形对应边的比叫做相似比.
(1)某同学在探究相似四边形的判定时,得到如下三个命题,请判断它们是否正确(直接在横线上填写“真”或“假”).
①条边成比例的两个凸四边形相似;( 命题)
②三个角分别相等的两个凸四边形相似;( 命题)
③两个大小不同的正方形相似.( 命题)
(2)如图1,在四边形ABCD和四边形A1B1C1D1中,∠ABC=∠A1B1C1,∠BCD=∠B1C1D1,
,求证:四边形ABCD与四边形A1B1C1D1相似.
(3)如图2,四边形ABCD中,AB∥CD,AC与BD相交于点O,过点O作EF∥AB分别交AD,BC于点E,F.记四边形ABFE的面积为S1,四边形EFDE的面积为S2,若四边形ABFE与四边形EFCD相似,求
的值.
(1)某同学在探究相似四边形的判定时,得到如下三个命题,请判断它们是否正确(直接在横线上填写“真”或“假”).
①条边成比例的两个凸四边形相似;( 命题)
②三个角分别相等的两个凸四边形相似;( 命题)
③两个大小不同的正方形相似.( 命题)
(2)如图1,在四边形ABCD和四边形A1B1C1D1中,∠ABC=∠A1B1C1,∠BCD=∠B1C1D1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2eacada1b71549c09a2dc12ea25f71f.png)
![](https://img.xkw.com/dksih/QBM/2019/7/18/2249564195569664/2250443429429248/STEM/04df74b0f90245beb495ae6ae6b375f7.png?resizew=429)
(3)如图2,四边形ABCD中,AB∥CD,AC与BD相交于点O,过点O作EF∥AB分别交AD,BC于点E,F.记四边形ABFE的面积为S1,四边形EFDE的面积为S2,若四边形ABFE与四边形EFCD相似,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5a9147b25285124851a61c7d1a24a.png)
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解答题-证明题
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名校
【推荐1】(1)已知:如图1,△ABC是⊙O的内接正三角形,点P为弧BC上一动点,求证:PA=PB+PC;
(2)如图2,四边形ABCD是⊙O的内接正方形,点P为弧BC上一动点,求证:PA=PC+
PB;
(3)如图3,六边形ABCDEF是⊙O的内接正六边形,点P为弧BC上一动点,请探究PA、PB、PC三者之间有何数量关系,并给予证明.
(2)如图2,四边形ABCD是⊙O的内接正方形,点P为弧BC上一动点,求证:PA=PC+
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(3)如图3,六边形ABCDEF是⊙O的内接正六边形,点P为弧BC上一动点,请探究PA、PB、PC三者之间有何数量关系,并给予证明.
![](https://img.xkw.com/dksih/QBM/2019/4/27/2191470212546560/2195233904091138/STEM/9cc29eacaa22406ea6963da7e4cda44c.png?resizew=385)
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解答题-问答题
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较难
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【推荐2】如图,在△ABC中,∠ABC=90°,BD⊥AC于D,∠CBD=α,AB=3,BC=4,求sinα,cosα,tanα的值.
![](https://img.xkw.com/dksih/QBM/2019/2/17/2142883438911488/2143951290744832/STEM/b780ff4abdfd497387d6f093b3bdf0b9.png?resizew=130)
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解答题-证明题
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名校
解题方法
【推荐3】如图1,等腰Rt△ABC中,∠BAC=90°,AB=AC=8,AD平分∠BAC交BC于点D,点E、F分别是线段AC、AB上两点,且AE=AF,连接BE交AD于点Q,过点F作FG⊥BE交BE于点P,交BC于点G;
(1)若BF=2,求DQ的长;
(2)求证:
;
(3)如图1,
,连接EF,将△EAF绕点A顺时针旋转,点M为EF中点,连接BM,CM,以BM为直角边构造等腰Rt△BMN,过点N作NR⊥BC交BC于点R,连接RM,当NR最小时,直接写出MR的长度.
(1)若BF=2,求DQ的长;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30882daf570752961c098be662b6a4a2.png)
(3)如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070bc896d35495237fd65576e9b6f88e.png)
![](https://img.xkw.com/dksih/QBM/2021/6/10/2740051595722752/2740244678352896/STEM/29d16430-6726-40ce-84cd-5f17d51ffc31.png?resizew=471)
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