1 . 如图,等边三角形
中,点
为直线
上一个动点,将线段
绕点
逆时针旋转
得到线段
,点
的对应点为点
,点
为线段
上一个动点,若
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
您最近一年使用:0次
名校
2 . 如图,在
中,
,
,
是
由绕点
顺时针旋转
得到,连接
,将
绕点
逆时针旋转
得到
,连接
.
;
(2)若
是等腰三角形,直接写出
的度数;
(3)当
三点共线时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f02cc86b7b971df364fdf47a0e75f1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba83afe4ade6624b283331a18bdf2ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c503e29373e8d87134bdb46bd3912910.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa15de8ed6842d6fd51176b51f4844da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6369cd1db768436809404b1f3c4132c0.png)
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3 . 【问题情景】
中,点E是线段
上一点(不与B,C点重合),连接
.将
绕点E顺时针旋转
得到
,连接
,求
的度数.
以下是两名同学通过不同的方法构造全等三角形来解决问题的思路:
小聪:过点
作
的延长线的垂线;小明:在
上截取
,使得
;
请你选择其中一名 同学的解题思路,写出完整的解答过程.
【类比探究】
(2)如图2,点E是菱形
边
上一点(不与B,C点重合),
,将
绕点E顺时针旋转
得到
,使得
,(
).
①求
的度数(用含
的代数式表示);
【学以致用】
②如图3,连接AF与CD相交于点G,当
时,若
,
,则BE的长为_____.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fc8bfdbf2a7e4ab5ef262b20611785.png)
以下是两名同学通过不同的方法构造全等三角形来解决问题的思路:
小聪:过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f8da1f66714eba7f2867a19d02479.png)
请你选择其中
【类比探究】
(2)如图2,点E是菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597ce705d3a2fe04d29de9e81ec6250d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce468e13528f3406d7ebb42cb7dae37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02cb0e46b861ad2cc17e7cb67416980.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fc8bfdbf2a7e4ab5ef262b20611785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
【学以致用】
②如图3,连接AF与CD相交于点G,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d03f73bec20b60bc7608972607f5a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e691e76614be733eee2f2845b298847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6f6c04bc017ced739230d14ba31948.png)
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4 . 如图,在
中,
.
分别为
上的动点,且
,连接
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015b221867c1b1eb53dc489421f418d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af70b81a82bd25f041bebf35933cc7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45de0916d8d18f2eb495e08e6bbc3016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74df87fcc553dcb1d4d042252383b037.png)
A.![]() | B.![]() | C.6 | D.![]() |
您最近一年使用:0次
2024-06-13更新
|
264次组卷
|
2卷引用:2024年江苏省无锡市滨湖区九年级中考一模数学试题
名校
5 . 如图1,
为
直径,
与
相切于点
,
交
于点
,点
为
的中点,连接
.
与
相切;
(2)如图2,连接
,若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)如图2,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a244bff7b6f96e12e9dbdbaca7d894b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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6 . 如图,平行四边形
的对角线
,
相交于点O,E,F分别是
,
的中点,连接
,
.
;
(2)若
,
,
.求平行四边形
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c6ae5c6098de9af49bb5c5e24bdee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b707c3d2dcf2f53fea4ef045dd8f295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-06-13更新
|
34次组卷
|
2卷引用:2024年甘肃省武威二十四中教研联片中考数学三模试题
2024九年级下·黑龙江哈尔滨·专题练习
7 . 如图,在正方形
中,O为对角线
的中点,E为正方形内一点,连接
,
,连接
并延长,与∠ABE的平分线交于点F,连接
,若
,则
的长度为___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a26c2c53046cbfe83f84f5393373589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
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8 . 如图,在
中,D是BC延长线上一点,且
,过点C作
且
,连接DE.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4a2a127d89d50d3fde881a9b58ef0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28971fe3e3f9d3849400e98b46fc3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85e359dd0247ef957a03a5e6d49aea6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fbb8974a5f907205d26b47b420bf4.png)
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9 . 如图,点E,F分别在平行四边形
的边
上,且
.
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd38e0d42026b953b2fd2ad3634ecb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c581dab991aeadf06d972e47673ea8.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e1dc3473ec67beb52aaaba5645cacb.png)
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2024-06-13更新
|
245次组卷
|
3卷引用:2024年山东省济南市槐荫区中考三模数学试题
真题
10 . 如图,在
中,
,
,
.A点P从点A出发、以
的速度沿
运动,同时点Q从点C出发,以
的速度沿
往复运动,当点P到达端点D时,点Q随之停止运动.在此运动过程中,线段
出现的次数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2594e927cb7ed022acc039c3bb136d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212063c7e452cd2bd0378d67929e3f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/182c408c62077540e26e779adf272444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ddd25759f63f954bb1e0e6b94fda1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f951a536cc785994e26d39407d20c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa9d494557857144d039a22f183525b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2cc58c4bf388e3b6c8dd34f62d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8896ed0102f70210e9ba146f09ca0665.png)
A.3 | B.4 | C.5 | D.6 |
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