1 . 如图1,在正方形
中,点E是
边上一点,F为
的中点,将线段
绕点F顺时针旋转
至线段
,连接
.某数学学习小组成员发现线段
与
之间存在一定的数量关系,并运用“特殊到一般”的思想开展了探究.
(1)①在上述两种思路中,选择其中一种完成其相应的第一步的证明:②写出线段
与
之间的数量关系式:______;
【深入探究】(2)如图1,当点E与点B不重合时,(1)中线段
与
之间的数量关系还成立吗?若成立,请加以证明:若不成立,请说明理由;
【拓展延伸】(3)连接
,记正方形
的面积为
,
的面积为
,当
是直角三角形时,请直接写出
的值.
![](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/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
思路一 | 思路二 | |
第一步 | 如图2,连接![]() ![]() ![]() | 如图3,将线段![]() ![]() ![]() ![]() ![]() |
第二步 | 利用相似三角形的性质及线段![]() ![]() ![]() ![]() | 利用全等三角形的性质及线段![]() ![]() ![]() ![]() |
图形表达 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
【深入探究】(2)如图1,当点E与点B不重合时,(1)中线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
【拓展延伸】(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7572ecc467c061ef71cf4486ec63ec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8305e23d5378f1cbf5518256a37c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2 . 综合探究
【初步探究】如图1,在正方形
中,点E是
边上一点(不与B,C重合),
于点G,交对角线
于点H,交
于点F.为了探究
与
之间的数量关系,在如图2中,作
,
交
的延长线于点M.
(1)如图2,①求证:
;②当
,
时,求证:
;
【类比迁移】(2)如图3,在矩形
中,
,
,
,
于点G,交
于点H,交
于点F.求
的值;
【拓展应用】(3)如图4,在等边三角形
中,
,E是
的中点,
,交
于点G,交
于点F.请直接写出
的值.
【初步探究】如图1,在正方形
![](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/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0ae50d5993a332b5cddb022eaa6f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93223650777bfa71643b387ea7217e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)如图2,①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80015669b216142fd64c9bde5747d4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783a833992e0862211a15fec2d3e3dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119b7f937fd3d31d3c7a3ef6cfc933e1.png)
【类比迁移】(2)如图3,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b41744ec71119e7264ef9673a35805a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a63c090c5041f4b78200915a9109e3.png)
【拓展应用】(3)如图4,在等边三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8689d619c2508c9000531fc1b8f1f21c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eaddfff30536c12b30caf9974feb59f.png)
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名校
3 . 综合与实践
问题情境:
数学活动课上,老师发给每位同学一个直角三角形纸片
,
,
,
.
问题发现
奋进小组将三角形纸片
进行以下操作:第一步:折叠三角形纸片
使点C与点A重合,然后展开铺平,得到折痕
;第二步:然后将
绕点D顺时针方向旋转得到
.点E,C的对应点分别是点F,G,直线
与边
交于点M(点M不与点A重合),与边
交于点N.
如图1小明发现,折痕
的长很容易求出,并且
和
的数量关系也能证明.
如图2小红发现,在
绕点D旋转的过程中,当直线
经过点B时或直线
时,
的长都可求…….
奋进小组根据小明和小红的发现,讨论后提出问题1和问题2,请你解答.
问题1:如图1,按照如上操作
(1)折痕
的长为______;
(2)在
绕点D旋转的过程中,试判断
与
的数量关系;并证明你的结论;
问题2:在
绕点D旋转的过程中,探究下列问题:
①如图2,当直线
经过点B时,
的长为______;
②如图3,当直线
时,求
的长;
拓展延伸:
小刚受到探究过程的启发,在
绕点D旋转的过程中,尝试画图,并提出问题3,请你解答.
问题3:在
绕点D旋转的过程中,连接
,当
取最小值时,请直接写出
的面积.
问题情境:
数学活动课上,老师发给每位同学一个直角三角形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
问题发现
奋进小组将三角形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ad83f1a3262048cba0e650b63e929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
如图1小明发现,折痕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
如图2小红发现,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95a2a2d3ead86a287255a428997c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
奋进小组根据小明和小红的发现,讨论后提出问题1和问题2,请你解答.
问题1:如图1,按照如上操作
(1)折痕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
问题2:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
①如图2,当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
②如图3,当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95a2a2d3ead86a287255a428997c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
拓展延伸:
小刚受到探究过程的启发,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
问题3:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2689f0ce5ab3467d8214794d8acb2bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101da161ae17652ccbe7d3f888762c2d.png)
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4 . 【探究发现】如图1,
中,点
分别在边
上,
,M为
中点,连结
并延长交
于点N,求证:
.
【拓展应用】如图2,四边形
中,
,对角线
交于N点,
分别是边
上的点,
交
于点M,若
,求
的值.
【综合提升】如图3,平行四边形
中,
,动点E在边
上,过E作
交
于点F,过F作
交
于点G,连结
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3648c864f9f58da1dbb166fee84cfeaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dc62e10004e73908091338362917da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b30a8f02b0532e55378662ebf23847.png)
【拓展应用】如图2,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989c75a3fd02e4971cab421c88de92f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137717f0e360e82319ced7e3a6c69b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c851c07c6e4b9a66e76168d6b16592e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b26abba429e10d15145337f8468660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e660f4bd9d1416b2c307b3fb0f2f37.png)
【综合提升】如图3,平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff9c30391df5d39a959e9f2c0be3a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c851c07c6e4b9a66e76168d6b16592e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bced1780d1fd068d0242fa11c18ed5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
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5 . 在学习图形的旋转时,创新小组同学们借助三角形和菱形感受旋转带来图形变化规律和性质.
【操作探究】
(1)如图1,已知
,
,将
绕着直角边
中点G旋转,得到
,当
的顶点D恰好落在
的斜边
上时,斜边
与
交于点H.
_________
②证明:
.
【问题解决】
(2)在(1)的条件下,已知
,
,求
的长.
【拓展提升】
(3)如图2,在菱形
中,
,
, 将菱形
绕着
中点M顺时针旋转,得到菱形
,当菱形
的顶点E分别恰好落在菱形
的
边和对角线
上时,菱形
的边与
边相交于点 N, 请直接写出
的长.
【操作探究】
(1)如图1,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69550d878381f6e8fb436e88638f070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db90c0feb35aa54464f1303be9118f37.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5a687a0635377e7e0e85d51c12f99.png)
【问题解决】
(2)在(1)的条件下,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
【拓展提升】
(3)如图2,在菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7cefa14a90337bbbb6e378d8a892d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4494a85de0be0b97a69348115aef8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454328a8e75953fdb0835ce80d9566e3.png)
![](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/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7cefa14a90337bbbb6e378d8a892d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c86b0118d4adeaf60493d13854fffc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9c0f5b073a60ec35e05583faea4ed7.png)
您最近一年使用:0次
2024-04-22更新
|
452次组卷
|
4卷引用:2024年广东省深圳市(33校联考)中考二模数学试题
2024年广东省深圳市(33校联考)中考二模数学试题(已下线)重难点05 四边形压轴类型归纳(9大题型+满分技巧+限时分层检测)-2024年中考数学【热点·重点·难点】专练(广东专用)数学(盐城卷)-【试题猜想】2024年中考考前最后一卷2024年四川省成都市石室天府中学九年级下学期中考三模数学试题
6 . 综合与实践
综合与实践课上,老师让同学们以“三角形与旋转”为主题开展数学活动.
【问题情景】如图,在
中,
是射线
上的一动点(不与点
重合),将线段
绕点
按顺时针方向旋转
得到
,连接
.
【问题探究】
(1)勤奋小组提出的问题:如图1,若
,则
之间的数量关系是______.
【类比延伸】
(2)智慧小组提出的问题:如图2,若
,探究
之间的数量关系.
【拓展探究】
(3)创新小组突发奇想,将问题迁移到平面直角坐标系中,如图3,若
,则在点
运动的过程中,当
时,请直接写出点
的坐标.
综合与实践课上,老师让同学们以“三角形与旋转”为主题开展数学活动.
【问题情景】如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8073465b2bfe822bc91d3b655fd3c923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd358585a317d08ef816ff357db49c8.png)
【问题探究】
(1)勤奋小组提出的问题:如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35733912d77e05487445e97b34fa52b3.png)
【类比延伸】
(2)智慧小组提出的问题:如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35733912d77e05487445e97b34fa52b3.png)
【拓展探究】
(3)创新小组突发奇想,将问题迁移到平面直角坐标系中,如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f40c2f0f89ad669e6fbfb5daafca83b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9817d6eaf6f9454152b2891f33aaa760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2024-04-18更新
|
133次组卷
|
2卷引用:2024年河南省濮阳市南乐县中考一模数学模拟试题
名校
7 . (1)证明推断:如图1,在正方形
中,点E,Q分别在边
上,
于点O,点G,F分别在边
上,
,求证:
;
(2)类比探究:如图2,在矩形
中,
,将矩形
沿
折叠,使点A落在
边上的点E处,得到四边形
,
交
于点H,连接
交
于点O,试探究
与
之间的数量关系,并说明理由;
(3)拓展应用:在(2)的条件下,连接
,若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd6877751384616819a8ddeef96c4133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8681dc7b0483bb527802389b03129b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70daa268c7a0b17f39c1e6eba043a3b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bbdea60708bebc259452cc5e07ea5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7b05f1f0d9dfcd37da1e437861aae6.png)
(2)类比探究:如图2,在矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483e5e695460e1752a7f9b0ee3f0b6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19191ca20cae3123d7df1b3a2ec5a857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)拓展应用:在(2)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313487069c46cb24487d6a48c0cc589a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a2e0b739038c0e756aa511920fa300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
8 . 综合与实践:
数学活动课上,同学们发现以下结论:如图
,已知等腰
和等腰
,其中
,射线
与
相交于点
,那么
和
数量关系是________,
和
位置关系是________;
【思考尝试】
如图
,已知四边形
和四边形
都是正方形,
是等腰直角三角形,
,连接
.同学们发现若能证明四边形
为平行四边形,即可找出
与
的数量关系.请你根据以上思路,直接写出
与
的数量关系________;
【实践探究】
如图
,四边形
和四边形
都是矩形,若
,连接
.求出
与
的数量关系;
【拓展迁移】
如图
,在【实践探究】的基础上,若
,
,如果
所在直线相交于点
,请直接写出矩形
绕点
旋转一周过程中
长度的最小值________.
数学活动课上,同学们发现以下结论:如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e7ba6e267dde1a65a98f9f36b585ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26813466e2ee49a493881a4384fc8748.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/a0ed1ec316bc54c37c4286c208f55667.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
【思考尝试】
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/0bc5c12b241539cc99487865f7d8bf34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee9a78b3e30a2fdec94bd07e0ed2de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b70b4115c3f2d6b2c0e76520e4cbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19232863167a25d31369eb862aa4c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
【实践探究】
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](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/2e0f551d8fd3dce44ca73727acff54ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897527a1aace2e9de1bb84bce69b086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
【拓展迁移】
如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9962e4b61d0a856eaeb32aa6f6864247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6655e2fa64a32cd12fe0279afd65d73.png)
您最近一年使用:0次
名校
9 . 【问题初探】
(1)如图1,等腰
中,
,点
为
边一点,以
为腰向下作等腰
,
,连接
,
,点
为
的中点,连接
.猜想并证明线段
与
的数量关系和位置关系.
(2)在(1)的条件下,如图2,将等腰
绕点B旋转,上述结论是否仍然成立?若成立,请证明;若不成立,请说明理由.
【拓展迁移】
(3)如图3,等腰
中,
,
.在
中,
,
.连接
,
,点
为
的中点,连接
.
绕点
旋转过程中,
①线段
与
的数量关系为:__________;
②若
,
,当点F在等腰
内部且
的度数最大时,线段
的长度为__________.
(1)如图1,等腰
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.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/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab34c8e368a7a2346a3922f5c532823d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd66f89184ca925f4575c26053decf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
(2)在(1)的条件下,如图2,将等腰
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab34c8e368a7a2346a3922f5c532823d.png)
【拓展迁移】
(3)如图3,等腰
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab34c8e368a7a2346a3922f5c532823d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd66f89184ca925f4575c26053decf2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fabdb76cad3e09a06f82a8ce80666c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab34c8e368a7a2346a3922f5c532823d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71989b96a7c7ade1879bbb9bd2cffb1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9ad150cb1e4cd8977d4cc3d99be17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd94dd51562ecbee6edd4265326b765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
您最近一年使用:0次
名校
10 . 定义:一组邻边相等且对角互补的四边形叫作“等补四边形”.如图1,四边形
中,
,
,则四边形
叫作“等补四边形”.
①在以下四种图形中,一定是“等补四边形”的是( )
A.平行四边形 B.菱形 C.矩形 D.正方形
②等补四边形
中,若
,则
;
③如图1,在四边形
中,
平分
,
,
.求证:四边形
是等补四边形.
(2)探究发现
如图2,在等补四边形
中,
,连接
,
是否平分
?请说明理由.
(3)拓展应用
如图3,在等补四边形
中,
,其外角
的平分线交
的延长线于点
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e8f68457b449d2860ecd3361753b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①在以下四种图形中,一定是“等补四边形”的是( )
A.平行四边形 B.菱形 C.矩形 D.正方形
②等补四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b5abfd7649b7acee7e1b33be0410e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2a8bf5e05a07c93a7104839fc21849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c3c112368d374afe3c2f8a4a1ce29c.png)
③如图1,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689196a03f24cc3cbe3a34bedbe38be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)探究发现
如图2,在等补四边形
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
(3)拓展应用
如图3,在等补四边形
![](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/1e37b078d02601f76f0f8320b410809f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640f058b479299659893cf524ddf6544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f21d8e7af78693e5da7957c8034e8bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
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