名校
解题方法
1 . 如图,四棱锥
中,底面ABCD为矩形,平面
平面ABCD,
,
,E,F分别为AD,PB的中点.求证:
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882847899779072/2920000285032448/STEM/8c22064922c74549955b4ec103b2c53f.png?resizew=242)
(1)
∥平面PCD;
(2)平面
平面PCD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882847899779072/2920000285032448/STEM/8c22064922c74549955b4ec103b2c53f.png?resizew=242)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
您最近一年使用:0次
2022-02-19更新
|
774次组卷
|
6卷引用:江西省永丰县永丰中学2020-2021学年高二上学期期中考试数学(理)试题
名校
解题方法
2 . 如图,已知四棱锥
的底面
是平行四边形,
,
,
,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
底面
,直线
与底面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/87c83e5c-68d3-4999-9b5b-a1defbf9a3c0.png?resizew=217)
(1)证明:平面
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae16b72924eb24c45f5dcfab07cc01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/87c83e5c-68d3-4999-9b5b-a1defbf9a3c0.png?resizew=217)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,已知四棱锥
的底面为菱形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2012/7/27/1570941975846912/1570941981491200/STEM/9b1df2a691784cb0bd3eb2b794c12f0f.png?resizew=215)
(
)求证:平面
平面
.
(
)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d82d07acbee5b207c7d053c422868f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fccf1cd8600af23d55876ab14e66e2d4.png)
![](https://img.xkw.com/dksih/QBM/2012/7/27/1570941975846912/1570941981491200/STEM/9b1df2a691784cb0bd3eb2b794c12f0f.png?resizew=215)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde1e200d1dd5ddc433c876c9d2f688c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f323421adf8083d252f0070f54f3a80.png)
您最近一年使用:0次
2016-12-01更新
|
953次组卷
|
6卷引用:2012年全国高中数学联赛河南赛区预赛试题
4 . 如图,在四棱锥
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869d3b18732c9b4b42887d003d7c497b.png)
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572916675854336/1572916681998336/STEM/219ab4b1758049db989d579ba3582596.png?resizew=146)
(Ⅰ)求证:平面
⊥平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413c799e8fb983e6274ec4be9ff6c431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869d3b18732c9b4b42887d003d7c497b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29470a095de205acb450d5a48b38be1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acb69f52b245011a41daaefd5b2a316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d97afe2733b75e9ea3de65c882f851c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572916675854336/1572916681998336/STEM/219ab4b1758049db989d579ba3582596.png?resizew=146)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
1634次组卷
|
9卷引用:第十四届高二试题(A卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
14-15高三上·江苏苏州·阶段练习
名校
解题方法
5 . 如图,在四面体
中,
,点
是
的中点,点
在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/2014/9/15/1571853775446016/1571853781057536/STEM/3fc8a4a257c84cf79e3185674f21220a.png?resizew=163)
(1)若
平面
,求实数
的值;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499e6009ac18b5770ff0bd96af67c56d.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a97d735a5a39a8243dbb93baa9d9089a.png)
![](https://img.xkw.com/dksih/QBM/2014/9/15/1571853775446016/1571853781057536/STEM/3fc8a4a257c84cf79e3185674f21220a.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e649e04994df61bf49c1c6599c3e7530.png)
您最近一年使用:0次
2016-12-03更新
|
1502次组卷
|
4卷引用:2015届江苏省广宇学校高三年级百强生竞赛文科数学试卷
2015届江苏省广宇学校高三年级百强生竞赛文科数学试卷2015届江苏省广宇学校高三年级百强生竞赛理科数学试卷(已下线)2015届江苏省苏州市高三9月调研考试数学试卷【全国百强校】江苏省海安高级中学2019届高三上学期第二次月考数学试题
解题方法
6 . 如图,在正方体
中,
、
分别为棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/2011/3/9/1570033655119872/1570033659871232/STEM/c415dd01a9fa47579744ff48e33fa6ee.png?resizew=197)
(1)求证:
平面
;
(2)求证:平面
⊥平面
;
(3)如果
,一个动点从点
出发在正方体的表面上依次经过棱
、
、
、
、
上的点,最终又回到点
,指出整个路线长度的最小值并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2011/3/9/1570033655119872/1570033659871232/STEM/c415dd01a9fa47579744ff48e33fa6ee.png?resizew=197)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a89b167e964aecdf9836ec6de5a911f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次