课本再现∶
思考:
我们知道,矩形的对角线相等,反过来,对角线相等的平行四边形是矩形吗?
可以发现并证明矩形的一个判定定理:对角线相等的平行四边形是矩形
已知:在
中, 对角线 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
求证:四边形
是矩形
(2)如图2, 若点
为矩形
边
延长线上一点,且
平分
,
,若
,求
的长为多少?
思考:
我们知道,矩形的对角线相等,反过来,对角线相等的平行四边形是矩形吗?
可以发现并证明矩形的一个判定定理:对角线相等的平行四边形是矩形
已知:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)如图2, 若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4598486f8c5ac28b1165b76e78105979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d5fcee996a47e9cc3cfd4ba108f21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
更新时间:2024-05-23 15:11:04
|
相似题推荐
解答题-作图题
|
适中
(0.65)
【推荐1】如图,在
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/33eda511-6ecd-403c-95fd-74bc597e7017.png?resizew=245)
(1)实践与操作:利用尺规作
的外接圆,圆心为点O(要求:尺规作图并保留作图痕迹,不写作法,标明字母).
(2)猜想与证明:若
,试猜想线段
与
半径r的数量关系,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/33eda511-6ecd-403c-95fd-74bc597e7017.png?resizew=245)
(1)实践与操作:利用尺规作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)猜想与证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c646c683fbe522edb7ea54fd3ad873d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】已知
是
的中线,取
的中点E,过点A作
,交
的延长线于点E.
是平行四边形;
(2)如图2,在(1)的条件下,连接
,交
于点O,过点O作
,交
的角平分线于点K,连接
、
,若
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/6095bae4840bfa80f2468f94b2002d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a5a2949b3d520ed03d57126c7d4d8d.png)
(2)如图2,在(1)的条件下,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a68e6aa34eed3fae5052942c2726908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868ff1350bd72625328c85c3097cd85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4c6b0869d7248b6c2f964718a67702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bd75fbe8bec72e27a3b3b6d48f138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021ff5673121d6c5804a66af60e7e9fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c836427f2d32d8f0f750b47d185269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】证明“直角三角形中,
角所对的边是斜边的一半.”如图,
中,
,
.
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3018c687427b6257767eda4a8c6612.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67462f8ecc8a4443134c1e86277c94e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/13/9b0a53e0-da4c-4844-bd22-4ceffbafe4e5.png?resizew=96)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在
中,
,D是直角边BC所在直线上的一个动点,连接AD,将AD绕点A逆时针旋转60°到AE,连接BE,DE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/28a237b6-a8d0-42a8-9257-d7c1d08f1902.png?resizew=418)
(1)如图1,当点E恰好在线段BC上时,请判断线段DE和BE之间的数量关系,并说明理由.
(2)当点E不在直线BC上时,如图2、图3,其他条件不变,(1)中的结论是否仍然成立?若成立,请在图2、图3中选择一个给予证明;若不成立,请直接写出新的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/28a237b6-a8d0-42a8-9257-d7c1d08f1902.png?resizew=418)
(1)如图1,当点E恰好在线段BC上时,请判断线段DE和BE之间的数量关系,并说明理由.
(2)当点E不在直线BC上时,如图2、图3,其他条件不变,(1)中的结论是否仍然成立?若成立,请在图2、图3中选择一个给予证明;若不成立,请直接写出新的结论.
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐3】在学习完勾股定理后,喜欢思考的小明想进一步探究直角三角形斜边的中线,他的思路是:
在
中,先作出直角边
的垂直平分线,并猜测它与斜边
的交点是中点,于是他把交点与点
连接,通过垂直平分线的性质以及等角对等边的代换,他发现了直角三角形斜边的中线与斜边的数量关系.
请根据小明的思路完成以下作图 与填空 :
用直尺和圆规作
的垂直平分线交
与点
,垂足为点
,连接
.(保留作图痕迹,不写作法)
已知:在
中,
,
垂直平分
,垂足为点
.
求证:
.
证明:
垂直平分
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e24c2bdad41127f07c6639a357d2b8.png)
① ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accb9dc1ba79e4195dd5699ee2855c57.png)
在
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
,
②
,
③ ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0574184df8079a4d1a45152cbb743da0.png)
.
.
通过探究,小明发现直角三角形均有此特征,请依照题意完成下面命题:
直角三角形斜边的中线 ④
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.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/c5db41a1f31d6baee7c69990811edb9f.png)
请根据小明的思路完成以下
用直尺和圆规作
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
已知:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c71622531dfa894f21b2da123d020d24.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50288ab167742c35976493d21531db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e24c2bdad41127f07c6639a357d2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accb9dc1ba79e4195dd5699ee2855c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](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/55f806322f1529fd8342d5778ebbebd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ed48f47be746e2584e555478d5dfd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c06422e1d55db3077257af113df4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df629488364255d931d38ee81ce104db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0574184df8079a4d1a45152cbb743da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffc824972f7280f5fbfad7cd05e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e16718e16f2ada58db490f442b44401.png)
通过探究,小明发现直角三角形均有此特征,请依照题意完成下面命题:
直角三角形斜边的中线 ④
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图,在菱形ABCD中,AB=4,∠ADN=60°,点E是AD边的中点,点M是AB边上一动点(不与点A重合),延长ME交射线CD于点N.连接MD、AN,
(1)求证:四边形AMDN是平行四边形;
(2)填空:
①当AM的值为_____时,四边形AMON是矩形;
②当AM的值为______时,四边形AMDN是菱形.
(1)求证:四边形AMDN是平行四边形;
(2)填空:
①当AM的值为_____时,四边形AMON是矩形;
②当AM的值为______时,四边形AMDN是菱形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/3c8d5a56-caf8-4a62-8941-6614edd85d77.png?resizew=146)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在Rt△ABC中,∠ACB=90°,CD⊥AB于D,过点C作CE∥AB,过点A作AE∥CD,两线相交于点E,连接DE.
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894337521229824/2894884774862848/STEM/8c3468198d8f4706a6205772912b9198.png?resizew=227)
(1)求证:四边形AECD是矩形;
(2)若
,求DE的长.
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894337521229824/2894884774862848/STEM/8c3468198d8f4706a6205772912b9198.png?resizew=227)
(1)求证:四边形AECD是矩形;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba52f545277ec2efdce2ce2a838c6136.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐1】如图,正方形
的边
在正方形
的边
上,连结
、
.
![](https://img.xkw.com/dksih/QBM/2015/7/24/1573884771213312/1573884777652224/STEM/ee986a8c93e04fff84635c827a3ba358.png)
(1)观察猜想
与
之间的大小关系,并证明你的结论;
(2)图中是否存在通过旋转能够互相重合的两个三角形?若存在,说出旋转过程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a8586ae37f043ee8d5162dec22126b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://img.xkw.com/dksih/QBM/2015/7/24/1573884771213312/1573884777652224/STEM/ee986a8c93e04fff84635c827a3ba358.png)
(1)观察猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
(2)图中是否存在通过旋转能够互相重合的两个三角形?若存在,说出旋转过程;若不存在,请说明理由.
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】如图,已知直线
交
轴于点
,交
轴于点
,抛物线
经过点
,与直线
交于
两点,点
为抛物线上的动点,过点
作
轴,交直线
于点
,垂足为
.
![](https://img.xkw.com/dksih/QBM/2020/9/27/2558370305548288/2564601415770112/STEM/047e3df777f2483d82471459df043f09.png?resizew=153)
(1)求抛物线的解析式;
(2)当点
位于抛物线对称轴右侧时,点
为抛物线对称轴左侧一个动点,过点
作
轴,垂足为点
.若四边形
为正方形时求点
的坐标;
(3)
关于抛物线对称轴对称,若
是以点
为顶角顶点的等腰直角三角形时,请直接写出点
的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca65ccb18d7867cbb8f0e436f49d122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d8de071a9c22c96a59b172d76c127e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca65ccb18d7867cbb8f0e436f49d122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6b93dbe5272a5167ff4e2918bec864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae95e96ce568efee50145f8d017353df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2020/9/27/2558370305548288/2564601415770112/STEM/047e3df777f2483d82471459df043f09.png?resizew=153)
(1)求抛物线的解析式;
(2)当点
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac5c9bc238d2eb0e735b0477417ffec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5d0a84fe728fdf9a44a15316499edab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adccd1dd14171c8c29d4a3836728c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次