观察猜想
![](https://img.xkw.com/dksih/QBM/2022/1/8/2897254795943936/2960831168135168/STEM/ccc1e64a-4e45-4876-9323-2252029eea23.jpg?resizew=439)
(1)如图1,在等边
中,点M是边
上任意一点(不含端点B、C),连接
,以
为边作等边
,连接
,则
与
的数量关系是______.
(2)类比探究
如图2,在等边
中,点M是
延长线上任意一点(不含端点C),(1)中其它条件不变,(1)中结论还成立吗?请说明理由.
(3)拓展延伸
如图3,在等腰
中,
,点M是边
上任意一点(不含端点B、C),连接
,以
为边作等腰
,使顶角
.连按
.试探究
与
的数量关系,并说明理由.
![](https://img.xkw.com/dksih/QBM/2022/1/8/2897254795943936/2960831168135168/STEM/ccc1e64a-4e45-4876-9323-2252029eea23.jpg?resizew=439)
(1)如图1,在等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474c0dc8c11624c4997e48b143bb09a5.png)
(2)类比探究
如图2,在等边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)拓展延伸
如图3,在等腰
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881f92487ba6848994dc3c7756665dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/474c0dc8c11624c4997e48b143bb09a5.png)
21-22九年级上·河南周口·期末 查看更多[5]
河南省周口市西华县2021-2022学年九年级上学期期末数学试题(已下线)专题4.45 三角形相似与旋转综合专题(培优篇)(专项练习)-2022-2023学年九年级数学上册基础知识专项讲练(北师大版)(已下线)专题27.42 相似三角形与旋转综合专题(培优篇)(专项练习)-2022-2023学年九年级数学下册基础知识专项讲练(人教版)(已下线)专题6.43 相似三角形与旋转综合专题(培优篇)(专项练习)-2022-2023学年九年级数学下册基础知识专项讲练(苏科版)(已下线)第12讲 相似三角形中的“手拉手”旋转型-【多题一解&一题多解】冲刺2023年中考数学满分应对方法与策略(全国通用)
更新时间:2022-04-18 14:49:20
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解答题-证明题
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【推荐1】如图,△ABC中,AB=AC,∠BAC=90°,点D是直线AB上的一动点(不和A、B重合),BE⊥CD于E,交直线AC于F
(1)点D在边AB上时,试探究线段BD、AB和AF的数量关系,并证明你的结论;
(2)点D在AB的延长线或反向延长线上时,(1)中的结论是否成立?若不成立,请写出正确结论并证明.
(1)点D在边AB上时,试探究线段BD、AB和AF的数量关系,并证明你的结论;
(2)点D在AB的延长线或反向延长线上时,(1)中的结论是否成立?若不成立,请写出正确结论并证明.
![](https://img.xkw.com/dksih/QBM/2019/1/14/2118554529726464/null/STEM/c5f18defae2d472398b779aeb41ba104.png?resizew=261)
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【推荐2】如图1,在矩形
中,
,E为边
上的动点,将矩形
沿直线
折叠,点A,B的对应点分别为点
.
时,则
;
(2)连接
,当
为直角三角形时,求
的长;
(3)设
与
的交点为点F,连接
,如图2,当四边形
为矩形时,求矩形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9911b76a2fe3477aad7682ea114db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1320d3b30daf11c5a7419983da3b3776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b795dd22b08ffb5567bff9892d78de23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32217457c4e96e2ef155cf15c1b65d97.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a21897349d3d7c94419692106887153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dbf33492e5223df78dea34a24ae015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a21897349d3d7c94419692106887153.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104fd0c1e8417ae5689d3c64910f4893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104fd0c1e8417ae5689d3c64910f4893.png)
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【推荐1】某数学兴趣小组开展了一次活动,过程如下:设
.现把小棒依次摆放在两射线之间,并使小棒两端分别落在射线
、
上.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2413009447215104/2413191434256384/STEM/c6e86d6f7ff3490091e5d4846a2030ae.png?resizew=552)
活动一、如图甲所示,从点
开始,依次向右摆放小棒,使小棒与小棒在端点处互相垂直(
为第1根小棒)
数学思考:
(1)小棒能无限摆下去吗?答: (填“能”或“不能”)
(2)设
,求
的度数;
活动二:如图乙所示,从点
开始,用等长的小棒依次向右摆放,其中
为第一根小棒,且
.
数学思考:
(3)若已经摆放了3根小棒,则
,
,
;(用含
的式子表示)
(4)若只能摆放5根小棒,则
的取值范围是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1b15a2711e4dea972d8d998ef4ef99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2020/3/5/2413009447215104/2413191434256384/STEM/c6e86d6f7ff3490091e5d4846a2030ae.png?resizew=552)
活动一、如图甲所示,从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
数学思考:
(1)小棒能无限摆下去吗?答: (填“能”或“不能”)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c224b06e9deeb1ab7978584dbf7ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
活动二:如图乙所示,从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566a0108be9644de1ec33e463d1d4d30.png)
数学思考:
(3)若已经摆放了3根小棒,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be24d4d6aea021e6ead6aeb0b9c252eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ce5f4c83c3fb130ff4956f0808a4f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f8efa19ebc1dc816e51635369c25c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(4)若只能摆放5根小棒,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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名校
【推荐2】已知在
中,∠ACB为锐角,点D为射线BC上一动点,连接AD,以AD为一边且在AD的右侧作等腰Rt
.
.解答下列问题:
(1)如果AB=AC,∠BAC=90°.
①如图1,当点D在线段BC上时(与点B不重合),线段CE,BD之间的位置关系为
②如图2,当点D在线段BC的延长线上时,①的结论是否仍然成立,如果不成立请说明理由,如果成立请加以说明.
(2)如果AB≠AC,∠BAC≠90°,点D在线段BC的延长线上时,试探究:
时(点C与点E重合除外),求:
的度数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296e23403c5727f1c64175b46966306d.png)
(1)如果AB=AC,∠BAC=90°.
①如图1,当点D在线段BC上时(与点B不重合),线段CE,BD之间的位置关系为
②如图2,当点D在线段BC的延长线上时,①的结论是否仍然成立,如果不成立请说明理由,如果成立请加以说明.
(2)如果AB≠AC,∠BAC≠90°,点D在线段BC的延长线上时,试探究:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4c0122aeefeaf1b75ce0b7062216df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ba22588c744c2b194f589b112b86bc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/2d21506a-5da1-4731-b88c-cb9f4b9bcb81.png?resizew=285)
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【推荐1】【问题】如图①,
和
都是等腰直角三角形,
,点D在
上.求证:
.
【感知】连接
,则
,
. 从而得出
为直角三角形,使问题得证. 请你根据以上思路,写出完整证明过程.
【应用】如图②,四边形
和四边形
都是正方形,点D在对角线
上.若
,
,正方形
的面积是 .
【拓展】如图③,
和
都是等边三角形,点A在
上,连接
.若
,
,请直接写出
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe4bdc5d9e833b23a1b916c06fc1a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ae31b70c84b0c8bf215843182a8c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba428d92833ec173c019c4324beed718.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/5f9545d8-82e9-4ae6-aaf9-b0526ed5441c.png?resizew=184)
【感知】连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42218a68301d770accaaefb96b19f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d135c9535e99a1f182cf4a01aa6e7a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0acc93490a6a784eb62201d93dd93d.png)
【应用】如图②,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e691e76614be733eee2f2845b298847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/e24cb6dc-2e88-437e-a7df-644a59954e95.png?resizew=184)
【拓展】如图③,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/4b1c8f1f-86c0-499c-b4a0-e1242d3fa2e7.png?resizew=136)
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解答题-问答题
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【推荐2】在平面直角坐标系中,
为原点,直角三角形
的顶点
,
,等边三角形
的一边
在
轴的负半轴上,点
在第二象限.将等边三角形
沿水平方向向右平移,顶点
,
,
的对应点分别为
,
,
.
在
轴的正半轴上,点
与原点
重合时,点
恰好落在边
上.填空:等边三角形
的边长等于______,点
的坐标为______.
(2)如图②,当
在
边上,且
,
分别与
相交于点
,
时,
与图中的哪条线段相等?
与图中的哪条线段相等?并证明你的结论:
(3)设
,等边三角形
与直角三角形
重叠部分的面积为
.当
时,求
的取值范围(直接写出结果即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fd4da08956db1f206c8ea026f4e52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1df17440481c8da8e0a17f008dbc4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820567942aa98b2feaaa017fcb7790df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/820567942aa98b2feaaa017fcb7790df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb2f87d7a79bd800f2650a670a46761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c049bdb31da2e5d8eefa8b7d135eb85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
(2)如图②,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb2f87d7a79bd800f2650a670a46761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c001be80e40e6278b294a694f9d6fb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cece895cbddf9d1f37f75e3b6346edda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd37244e07a7f1e6b0d8afdb469cf76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142e0f0e25dc2ad81ec1a7ec6ed866b.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec5b34559d44ba345133399644b485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c049bdb31da2e5d8eefa8b7d135eb85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8449c227579a276f83ce486d47ce09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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【推荐3】如图1,Rt△ABC中,∠ACB=90°,D为AB的中点,∠EDF=90°,DE交AC于点G,DF经过点C.
![](https://img.xkw.com/dksih/QBM/2016/9/28/1574244609146880/1574244615036928/STEM/54672418496f46448d8fe210280dc83e.png)
(1)若∠B=60°.
①求∠ADE的度数;
②如图2,将图1中的∠EDF绕点D顺时针方向旋转角α(0°<α<60°),旋转过程中的任意两个位置分别记为∠E1DF1,∠E2DF2,DE1交直线AC于点P,DF1交直线BC于点Q,DE2交直线AC于点M,DF2交直线BC于点N,求
的值;
(2)将(1)问中的“若∠B=60°”改为“∠B=β(60°<β<90°)”,其余条件不变,判断
的值是否为定值,如果是,请直接写出这个值(用含β的式子表示);如果不是,请说明理由.
![](https://img.xkw.com/dksih/QBM/2016/9/28/1574244609146880/1574244615036928/STEM/54672418496f46448d8fe210280dc83e.png)
(1)若∠B=60°.
①求∠ADE的度数;
②如图2,将图1中的∠EDF绕点D顺时针方向旋转角α(0°<α<60°),旋转过程中的任意两个位置分别记为∠E1DF1,∠E2DF2,DE1交直线AC于点P,DF1交直线BC于点Q,DE2交直线AC于点M,DF2交直线BC于点N,求
![](https://img.xkw.com/dksih/QBM/2016/9/28/1574244609146880/1574244615036928/STEM/c480eb9cbbf14fdcb2dcefab631eb4ce.png)
(2)将(1)问中的“若∠B=60°”改为“∠B=β(60°<β<90°)”,其余条件不变,判断
![](https://img.xkw.com/dksih/QBM/2016/9/28/1574244609146880/1574244615036928/STEM/6483f7e3929747438bbdbd966196b6ba.png)
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【推荐1】如图,在矩形
中,
,对角线
、
交于点
,点
为对角线
上一点,连接
,在
内部作射线
与线段
交于点
(不与点
、点
重合)、与线段
交于点
,且
.
![](https://img.xkw.com/dksih/QBM/2022/11/14/3109511539015680/3111023501647872/STEM/7bffe74782714a08bbe29151d51fdcac.png?resizew=389)
(1)当
,求
的正切值;
(2)射线
交射线
与点
,若
,求
的长;
(3)设线段
,
,写出
关于
的函数关系式,并写出取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248de7a6a4b79d317d02eb343096f186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d76e136e7df3692ae6536fc70b6961a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a689046bc30d6cfc7501d2a6559abdd.png)
![](https://img.xkw.com/dksih/QBM/2022/11/14/3109511539015680/3111023501647872/STEM/7bffe74782714a08bbe29151d51fdcac.png?resizew=389)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09307b2858ce8da4bca9a519de9350ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa33f3d7f434fb88b2af25e6411dd507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
(3)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d794fa98ade13e9a141b45a139844914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db2394f161af156e2b037183e5b010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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【推荐2】如图①,直线y=-
x+3与x轴相交于点A,与y轴相交于点B,点C(m,n)是第二象限内一点,以点C为圆心的圆与x轴相切于点E,与直线AB相切于点F.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
(1)当四边形OBCE是矩形时,求点C的坐标;
(2)如图②,若⊙C与y轴相切于点D,求⊙C的半径.
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名校
【推荐3】如图,已知矩形OABC,点P在边OA上(不与端点重合),点Q在边CO上(不与端点重合).
(1)如图(1),若∠BPQ=90°,且△OPQ与△PAB和△QPB相似,请写出表示这三个三角形相似的式子,并探究此时线段OQ、QB、BA之间的数量关系.
(2)若∠PQB=90°,且△OPQ与△PAB、△QPB都相似,如图(2),请重新写出表示这三个三角形相似的式子,并证明AB:OA=2
:3.
(3)在(1)中,若OA=8
,OC=8,OP=
CQ.以矩形OABC的两边OA、OC所在的直线分别为x轴和y轴,建立平面直角坐标系,如图(3),若某抛物线顶点为P,点B在抛物线上.
①求此抛物线的解析式.
②过线段BP上一动点M(点M与点P、B不重合),作y轴的平行线交抛物线于点N,若记点M的横坐标为m,试求线段MN的长L与m之间的函数关系式,画出该函数的示意图,并指出m取何值时,L有最大值,最大值是多少?
(1)如图(1),若∠BPQ=90°,且△OPQ与△PAB和△QPB相似,请写出表示这三个三角形相似的式子,并探究此时线段OQ、QB、BA之间的数量关系.
(2)若∠PQB=90°,且△OPQ与△PAB、△QPB都相似,如图(2),请重新写出表示这三个三角形相似的式子,并证明AB:OA=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(3)在(1)中,若OA=8
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
①求此抛物线的解析式.
②过线段BP上一动点M(点M与点P、B不重合),作y轴的平行线交抛物线于点N,若记点M的横坐标为m,试求线段MN的长L与m之间的函数关系式,画出该函数的示意图,并指出m取何值时,L有最大值,最大值是多少?
![](https://img.xkw.com/dksih/QBM/2019/2/19/2144298860371968/2144900990517248/STEM/1fa7db1e5360451cb1374a512cba6e84.png?resizew=484)
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