1 . 矩形
中,
,
,将矩形折叠,使点A落在点P处,折痕为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/3fe4a135-a170-4633-9ab1-dc2b7c6a7aea.jpg?resizew=309)
(1)观察发现:如图1,若点P恰好在边
上,
________(填写一个与
相似的三角形);
(2)拓展探究:如图1,若点P恰好在边
上,则线段
的长为________.
(3)迁移应用:如图2,若E是
的中点,
的延长线交
于点F,其余条件不变,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdf82f2b3ac77ee7b9b35aebe0dd83f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/3fe4a135-a170-4633-9ab1-dc2b7c6a7aea.jpg?resizew=309)
(1)观察发现:如图1,若点P恰好在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4017202addef8e8a016ba3373d1cf926.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48775f13f05443e6f6d30ae26e669f5.png)
(2)拓展探究:如图1,若点P恰好在边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)迁移应用:如图2,若E是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
解题方法
2 . 综合与实践
操作探究
(1)如图1,将矩形
折叠,使点
与点
重合,折痕为
,
与
交于点
.请回答下列问题:
①与
全等的三角形为______,与
相似的三角形为______.并证明你的结论:(相似比不为1,只填一个即可):
②若连接
、
,请判断四边形
的形状:______.并证明你的结论;
拓展延伸
(2)如图2,矩形
中,
,
,点
、
分别在
、
边上,且
,将矩形折叠,使点
与点
重合,折痕为
,
与
交于点
,连接
.
①设
,
,则
与
的数量关系为______;
②设
,
,请用含
的式子表示
:______;
③
的最小值为______.
操作探究
(1)如图1,将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00870385ca7f3214e2971779eb4c7904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00870385ca7f3214e2971779eb4c7904.png)
②若连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9766e5eb6796dafc5ffe212afdfc43c0.png)
拓展延伸
(2)如图2,矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4817c12128c0d81f54e9529cb0a3588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417af7fd8533934a0d5b280408e15d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aac645b73f767aa10cdd3359842798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce629f210d757b89a726d2ae851f9ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da49a7a7feead3a9584e503cfde55a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/ddea6cbc-e094-40e0-ad34-b89a895a05ce.png?resizew=409)
您最近一年使用:0次
名校
解题方法
3 . 如图1,在
中,
,
,点
、
分别是边
、
上的点,且
,将
绕点
按顺时针方向旋转,记旋转角为
.
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/22802a5e43df4bf1a22250e0a54afc68.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/ef11e5e790b14004a6d60a13ab79cba6.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/5d171d9c68c24d1f824401ac851bc6e7.png?resizew=180)
(1)问题发现:如图1,当
时,
________;
(2)拓展探究:试判断:当
时,
的大小有无变化?请仅就图2的情形给出证明;
(3)问题解决:若
为
内一点,且
,请直接写出线段
、
、
之间的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f149e83812e72efd7dd3dfc78d0134ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f4bcb7ddcdbb66f0304d0531e84c6d.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5f2480cca3544103abb5f6a29b4554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/22802a5e43df4bf1a22250e0a54afc68.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/ef11e5e790b14004a6d60a13ab79cba6.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2020/10/21/2575847163789312/2576330636451840/STEM/5d171d9c68c24d1f824401ac851bc6e7.png?resizew=180)
(1)问题发现:如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6c149a5bccb793dd3014691896e414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787f35ca2d29a1cebb5c98c488b723b7.png)
(2)拓展探究:试判断:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de68f4f738ecd4e153c9f480c8f040b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1682a8242948cc1d76eddef3e50836f.png)
(3)问题解决:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d0c6f6c7fce47f41d562abcb6c6c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
4 . 【问题情境】在△ABC中,BA=BC,∠ABC=α(0°<α<180°),点P为直线BC上一动点(不与点B、C重合),连接AP,将线段PA绕点P顺时针旋转得到线段PQ旋转角为α,连接CQ.
![](https://img.xkw.com/dksih/QBM/2020/6/4/2477151729295360/2478054974136320/STEM/6c9181c6d4d7485ba538db590aeb1a28.png?resizew=479)
【特例分析】(1)当α=90°,点P在线段BC上时,过P作PF∥AC交直线AB于点F,如图①,易得图中与△APF全等的一个三角形是 ,∠ACQ= °.
【拓展探究】(2)当点P在BC延长线上,AB:AC=m:n时,如图②,试求线段BP与CQ的比值;
【问题解决】(3)当点P在直线BC上,α=60°,∠APB=30°,CP=4时,请直接写出线段CQ的长.
![](https://img.xkw.com/dksih/QBM/2020/6/4/2477151729295360/2478054974136320/STEM/6c9181c6d4d7485ba538db590aeb1a28.png?resizew=479)
【特例分析】(1)当α=90°,点P在线段BC上时,过P作PF∥AC交直线AB于点F,如图①,易得图中与△APF全等的一个三角形是 ,∠ACQ= °.
【拓展探究】(2)当点P在BC延长线上,AB:AC=m:n时,如图②,试求线段BP与CQ的比值;
【问题解决】(3)当点P在直线BC上,α=60°,∠APB=30°,CP=4时,请直接写出线段CQ的长.
您最近一年使用:0次
解题方法
5 . 【提出问题】
(1)已知:菱形ABCD的边长为6,
,
为等边三角形,当点P与点D重合,点E在对角线AC上时(如图1所示),求
的值.
【类比探究】
(2)在上面的问题中,如果把点P沿DA方向移动,使
,其余条件不变(如图2),求
的值;
【拓展迁移】
(3)在原问题中,当点P在线段DA的延长线上,点E在CA的延长线上时(如图3),设
,请直接写出线段AE、AF的长与m有怎样的数量关系.
(1)已知:菱形ABCD的边长为6,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577250c86a14c7a2990bf9852c7213d5.png)
【类比探究】
(2)在上面的问题中,如果把点P沿DA方向移动,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577250c86a14c7a2990bf9852c7213d5.png)
【拓展迁移】
(3)在原问题中,当点P在线段DA的延长线上,点E在CA的延长线上时(如图3),设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbd4869dbffe2c1d53ab6b2494de547.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/bc34254e-1ee5-450d-8b61-610037a0cf41.png?resizew=452)
您最近一年使用:0次
真题
6 . 在
中,
,
.点D在边
上,
且
,
交边
于点F,连接
.
![](https://img.xkw.com/dksih/QBM/2020/7/20/2509893064163328/2509931362967552/STEM/85f2eaebaec34b16aa3f06383dcac97a.png?resizew=650)
(1)特例发现:如图1,当
时,①求证:
;②推断:
_________.;
(2)探究证明:如图2,当
时,请探究
的度数是否为定值,并说明理由;
(3)拓展运用:如图3,在(2)的条件下,当
时,过点D作
的垂线,交
于点P,交
于点K,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3757794aa3436f7774257a8d72fabe4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518586d91b63569fc317b323835a0c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/2020/7/20/2509893064163328/2509931362967552/STEM/85f2eaebaec34b16aa3f06383dcac97a.png?resizew=650)
(1)特例发现:如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4e363bfd418579e6229230df034bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494bf14f8369edcb5ba24413e91fd473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfbc2a377c4d6c0423744c3b63409b6.png)
(2)探究证明:如图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37c9d3a0b6a35923425a3bc9c0706ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a2db6311e228ed33b6c71d0a5918cf.png)
(3)拓展运用:如图3,在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ca4eca8f3c7e8bd1a37b04860e0850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.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/b2daff42e1907ed02b20096c4047ac39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
您最近一年使用:0次
2020-07-20更新
|
1242次组卷
|
3卷引用:湖北省襄阳市2020年中考数学试题
解题方法
7 . 在
中,
,经过点B的直线l(l不与直线
重合)与直线
的夹角等于
,分别过点C、A作直线l的垂线,垂足分别为点D、E.
(1)问题发现:
①若
,如图①,则
________;
②若
,如图②,则
________;
(2)拓展探究:当
时,
的值有无变化?请仅就图③的情形给出证明;
(3)问题解决:若直线
、
交于点F,
,
,请直接写出线段
的长.
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(1)问题发现:
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb01d2b57580731c8b807ac8cffc8ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787f35ca2d29a1cebb5c98c488b723b7.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42ed2e5bd5a0f033e24008697bf4963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787f35ca2d29a1cebb5c98c488b723b7.png)
(2)拓展探究:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c328690bedf40f97f00359b316ddbda9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1682a8242948cc1d76eddef3e50836f.png)
(3)问题解决:若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f482a3c73fc7eb87b611702e6fe2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/515c6b00-6e55-44d9-994c-67f4577873ca.png?resizew=343)
您最近一年使用:0次
2020-06-04更新
|
71次组卷
|
5卷引用:2016届河南省中考定心模拟数学试卷
2016届河南省中考定心模拟数学试卷江苏省靖江市外国语学校2018-2019学年第一学期九年级上期中数学试题(已下线)【万唯原创】2016年份河南省中考数学定心卷-普通高中招生考试定心卷(已下线)【万唯原创】2017年河南省中考数学逆袭卷-逆袭诊断卷(已下线)【万唯原创】河南省2020年中考数学-逆袭卷-特训22-23
真题
名校
8 . (1)证明推断:如图(1),在正方形
中,点
,
分别在边
,
上,
于点
,点
,
分别在边
,
上,
.
①求证:
;
②推断:
的值为 ;
(2)类比探究:如图(2),在矩形
中,
(
为常数).将矩形
沿
折叠,使点
落在
边上的点
处,得到四边形
,
交
于点
,连接
交
于点
.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
,当
时,若
,
,求
的长.
![](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/acc290b44635265137fdf13146b6a6d9.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/8681dc7b0483bb527802389b03129b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bbdea60708bebc259452cc5e07ea5a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e6ecc67e184645d2cde587f8aa8f76.png)
②推断:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f12d3876f1b0ffaf9179fb85c0e683.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/714c979d980d5377a6cc93a452bffe8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/73465a1f9aa03481295bf6bd3c6903ac.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/1dde8112e8eb968fd042418dd632759e.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/92d71107894329b293117036013dcbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2f30860874820bca1a0a62d28f2095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e6edb9dbe91787f764cf056bbfa8d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/3/cfbf55e6-36da-4181-b6d0-663a0a4a0c43.png?resizew=261)
您最近一年使用:0次
2019-07-26更新
|
1698次组卷
|
12卷引用:湖北省襄阳市2019年中考数学试题
湖北省襄阳市2019年中考数学试题2020年四川省成都七中万达学校中考数学三模试题2020年湖南省岳阳市中考一模数学试题(已下线)【万唯原创】2020年河南省中考数学试题-河南试题正文-第二部分重难题型32021年安徽省滁州市定远县中考一模数学试题浙江省宁波市鄞州区九校联考2021-2022学年九年级下学期月考数学试题(一模)2022年浙江省衢州市柯城区九年级第二次模拟考试数学试题2023年河南省南阳市淅川县中考一模数学试题2022年广东省珠海市梅华中学中考三模数学试题(已下线)2023年河南省一模(几何综合2)广东省深圳市北师大南山附属学校中学部2023-2024学年九年级下学期开学考数学试题山东省初中毕业年级2024年数学模拟预测题
名校
9 . 【基础巩固】
(1)如图1,在
中,D为
上一点,连结
,E为
上一点,连结
,若
,求证:
.
【尝试应用】
(2)如图2,在平行四边形
中,对角线
交于点O,E为
上一点,连结
,若
,求
的长.
【拓展提升】
(3)如图3,在菱形
中,对角线
交于点O,E为
中点,F为
上一点,连结
,若
,
,求菱形
的边长.
(1)如图1,在
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aadef7d71079f7953ea6eb3f9c44968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd7edc508c8fc8de42058bd2364d77a.png)
【尝试应用】
(2)如图2,在平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d0b0b7d07ac1aebab6b6f1e8c6acdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5168d2641ae584f6b922074320762f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ba99f3d174abf75fa5c9707f107145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
【拓展提升】
(3)如图3,在菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d0b0b7d07ac1aebab6b6f1e8c6acdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1992f6d926022aa72f86d367da4bc8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511588db7f353f450c7a3a60135d699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
10 . ●问题发现
如图1,
和
都是等边三角形,边
和
在同一直线上,
是边
的中点,
,连接
,则下列结论正确的是__________.(填序号即可)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b62eb049-7dac-45cb-bcbb-eb9449b02b3b.png?resizew=825)
①
;②
;③
;④整个图形是轴对称图形.
●数学思考
将图1中的
绕着点
旋转,
不动,连接
和
,如图2,则
和
具有怎样的数量和位置关系?请给出证明过程;
●拓展应用
已知
,
,在图1中的
绕着点
旋转的过程中,当
时,求线段
的长度.
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b62eb049-7dac-45cb-bcbb-eb9449b02b3b.png?resizew=825)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf2e3236ea30ee2c37928b98041f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c503e29373e8d87134bdb46bd3912910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
●数学思考
将图1中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
●拓展应用
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee49e97546d466ba3ee630e08cdc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c750cbbbe03c2d4fb2b4ea84f659631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c252a0fe067d434a2b5aeac011b9914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2023-03-25更新
|
332次组卷
|
4卷引用:2023年江西省南昌市青山湖区九年级下学期3月质量调研数学试卷
2023年江西省南昌市青山湖区九年级下学期3月质量调研数学试卷(已下线)专题01 与旋转有关的计算(30题)-【帮课堂】2023-2024学年九年级数学上册同步学与练(人教版)(已下线)2023年江西一模(几何综合)江西省宜春市丰城市丰城中学2023-2024学年九年级下学期开学考试数学试题