解题方法
1 . 已知空间四边形ABCD中,E、F、G、H分别是AB、BC、CD、DA的中点,且AC=BD.
(1)判断四边形EFGH的形状,并加以证明;
(2)求证:
平面EFGH.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/23a2906c-fad3-44b8-9a83-1f4d47fc6612.png?resizew=135)
(1)判断四边形EFGH的形状,并加以证明;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f306ff6d237cd9d847aa109acf9333d7.png)
您最近一年使用:0次
解题方法
2 . 如图,在三棱柱
中,若G,H分别是线段
,
的中点.
![](https://img.xkw.com/dksih/QBM/2023/7/7/3275930420338688/3277428222746624/STEM/014c9cac2e2c428193f7c5750edce478.png?resizew=205)
(1)求证:
//面
.
(2)在线段
上是否存在一点
,使得平面
//平面
,若存在,指出
的具体位置并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0147945bdf3db4bf5e40be746ef2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/2023/7/7/3275930420338688/3277428222746624/STEM/014c9cac2e2c428193f7c5750edce478.png?resizew=205)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
3 . 在四棱锥
中,
平面ABCD,
,
.
(1)证明:
平面
;
(2)若
是
的中点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7252c9e3a1aebe1b31d080ac7ea725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b802b67ff805001ac88a6c85a795c07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/22/2186bddd-12a8-473a-b3db-34fb1ca2c552.png?resizew=129)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
名校
解题方法
4 . 在如图1所示的等腰梯形
中,
,将它沿着两条高
折叠成如图2所示的四棱锥
(
重合),点
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/22/a7ff9d63-de49-4325-b090-b97326536a7a.png?resizew=366)
(1)证明:
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791ab4542eec7e4056b56fe36d50657e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/22/a7ff9d63-de49-4325-b090-b97326536a7a.png?resizew=366)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eaa5e336f830a3e5cd60ff7a756f3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e8906c3d5e9f8ee0523a650d20001f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823f4e614dd9290178c2b9c9fd2460a2.png)
您最近一年使用:0次
2022-06-20更新
|
1146次组卷
|
6卷引用:新疆克拉玛依市高级中学2021-2022学年高一下学期期末数学试题
新疆克拉玛依市高级中学2021-2022学年高一下学期期末数学试题河南省安阳市2021-2022学年高一年级下学期阶段性测试(五)数学试卷(已下线)知识点 空间几何体的结构 易错点5 混淆翻折问题前后变与不变(已下线)7.2 空间几何中的垂直(精讲)(已下线)8.6.3 平面与平面垂直(精讲)(已下线)专题四 期末高分必刷解答题(32道)-《考点·题型·密卷》
名校
解题方法
5 . 如图,已知棱柱
的底面是平行四边形,且侧面均为正方形,F为棱
的中点,M为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987673485484032/2988246579707904/STEM/771fd68a-3558-494e-8618-ffd5d9d94c18.png?resizew=156)
(1)作出面
与面
的交线并证明.
(2)求证:
面ABCD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987673485484032/2988246579707904/STEM/771fd68a-3558-494e-8618-ffd5d9d94c18.png?resizew=156)
(1)作出面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fa54ff714b0a8ebe5bf167b1e037fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aab7ac63e498d43b93ba40426bf204.png)
您最近一年使用:0次
2022-05-27更新
|
1286次组卷
|
5卷引用:新疆生产建设兵团第二中学2021-2022学年高一下学期期末考试卷数学试题
新疆生产建设兵团第二中学2021-2022学年高一下学期期末考试卷数学试题广东实验中学2021-2022学年高一下学期期中数学试题(已下线)第11练 空间直线、平面的平行-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)广东省佛山市南海区南海中学2022-2023学年高一下学期第二次阶段考数学试题宁夏大武口区石嘴山市第三中学2022-2023学年高一下学期期中数学试题
6 . 用适当的方法证明下列命题,求证:
(1)
;(
)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840ab5202c0dd51fb0d9aa14a500fd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eb9b6fe8959ae9e71e857b6d6fed49.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734f585f8cfc92522f6daf997ebec04d.png)
您最近一年使用:0次
2021-10-03更新
|
805次组卷
|
5卷引用:新疆新源县2020-2021学年高二下学期期末数学(文)试题
7 . 已知三棱柱
(如图所示),底面
是边长为2的正三角形,侧棱
底面
,
,
为
的中点.
为
的中点,求证:
平面
;
(2)证明:
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78870dc2f09416598a67ff7c61023a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea124cef7ab3fd8069243e9894d1c59.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4557a368725226f2c8ea2efb7d30e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641d9688e81760c02d0dfc4ba015afb1.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd5d1b72eccfb437d85ae09382026ee.png)
您最近一年使用:0次
2020-09-27更新
|
5977次组卷
|
16卷引用:新疆哈密市第八中学2021-2022学年高二上学期期末考试数学(文)试题
新疆哈密市第八中学2021-2022学年高二上学期期末考试数学(文)试题四川省成都市蓉城名校联盟2018-2019学年高一下学期期末联考数学试题四川省蓉城名校联盟2018-2019学年高一下学期期末数学(文)试题山东省聊城市九校2020-2021学年高二上学期第一次开学联考数学试题安徽省阜阳市太和第一中学2020-2021学年高二(普通班)上学期期中数学试题安徽省阜阳市太和第一中学2020-2021学年高二(奥赛班)上学期期中数学试题宁夏吴忠市吴忠中学2020-2021学年高二3月月考数学(文)试题云南省昆明市官渡区第一中学2021-2022学年高二上学期开学考数学试题河南省新乡市辉县市第一高级中学2020-2021学年高一下学期第一次阶段性考试数学试题(已下线)期末考测试(提升)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)安徽省六安第一中学2021-2022学年高一下学期期中数学试题(已下线)高一下学期数学期末考试高分押题密卷(二)-《考点·题型·密卷》河南市柘城县德盛高级中学2022-2023学年高一下学期6月月考数学试题 陕西省宝鸡市扶风县法门高中2023-2024学年高一下学期期中考试数学试卷陕西省咸阳市武功县普集高级中学2023-2024学年高一下学期第3次月考数学试题黑龙江省牡丹江市第二高级中学2023-2024学年高一下学期第二次月考数学试卷
解题方法
8 . 证明:(1)已知a,b,
,
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知a,b,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede693e9fed26c40f6fee9c3aaad147c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede693e9fed26c40f6fee9c3aaad147c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f917a19a15bceb9a3769e59e25dd9c.png)
您最近一年使用:0次
2020-09-01更新
|
207次组卷
|
2卷引用:新疆阿勒泰地区2019-2020学年高二下学期期末考试数学试题(A卷)
名校
解题方法
9 . 已知数列
中,
,其前
项的和为
,且满足
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d398667a473f002e284c13f36296633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5781327c6d27ab4ba78d9b4cbafe69.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83668ff336589f82a2cd04db9f9947.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd89451960be3eff4a971c8db8c9da48.png)
您最近一年使用:0次
2017-10-10更新
|
1016次组卷
|
2卷引用:新疆维吾尔自治区乌鲁木齐市实验学校2023-2024学年高二上学期期末数学试题