1 . 如图,在直三棱柱
中,平面
平面
,
(1)求证:
平面
;
(2)若直线
与平面
所成角为
,二面角
的大小为
,试判断
,
的大小关系,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/343133ce-be69-465f-a40d-f27986bac88b.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185729402f3b20ac3e0b003be9b385eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
您最近一年使用:0次
名校
解题方法
2 . 在四面体
中,点H为
的垂心,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/6104b9ec-b57c-4e0d-b7b6-aeab1f4512f8.png?resizew=164)
(1)若
,求证:
;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/11/6104b9ec-b57c-4e0d-b7b6-aeab1f4512f8.png?resizew=164)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dee6c1410e79934b560642684807e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2298257c6a39a4ac916cee3858cd10e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c9c32921b9f678056406dbb27fd9b.png)
您最近一年使用:0次
2023-05-20更新
|
491次组卷
|
2卷引用:广东省阳江市两阳中学2022-2023学年高一下学期期末数学试题
名校
解题方法
3 . 如图所示,四棱锥
的底面是边长为1的正方形,
,E为
上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/d5a2014a-22ca-4d3a-bcd3-26bf77127c50.png?resizew=154)
(1)求证:
平面
;
(2)在侧棱
上是否存在一点F,使得
平面
?若存在,指出F点的位置,并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e896ec179a48561a0671416340ddfc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcbbbe350b38381d1999e2886d45f0e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/d5a2014a-22ca-4d3a-bcd3-26bf77127c50.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
您最近一年使用:0次
2022-09-15更新
|
1841次组卷
|
5卷引用:广东省佛山市超盈实验中学2022-2023学年高二上学期第一次学科素养监测数学试题
解题方法
4 . 如图所示,四棱锥
的底面是边长为1的正方形,
为
上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/ef37ee78-bf0d-45f4-b914-6a75bcb8ac9d.png?resizew=178)
(1)求证:
平面
;
(2)在侧棱
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
平面
?若存在,指出
点的位置,并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff895634f4d8dd3d874791df72446e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b889dc32aa6996c840ff964ac2c546.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/ef37ee78-bf0d-45f4-b914-6a75bcb8ac9d.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
解题方法
5 . 如图,在
中.
,
,
,
,
分别是
,
上的点,且
,将
沿
折起到
的位置,使
,如图.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/81e871b2-adbd-4d6e-a3e6-13726f46f5c0.png?resizew=184)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/78d41032-17be-4219-8611-ddeeb6c14280.png?resizew=168)
(1)求证:BC⊥平面
;
(2)若
,
为
的中点,作出过
且与平面
平行的截面,并给出证明;
![](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/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e210c9698063925ad2df6b6c1749571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffbf41f3890efb6956907ad3c4062a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/81e871b2-adbd-4d6e-a3e6-13726f46f5c0.png?resizew=184)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/78d41032-17be-4219-8611-ddeeb6c14280.png?resizew=168)
(1)求证:BC⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
11-12高二上·广东·期中
真题
解题方法
6 . 如图,平行六面体
的底面
是菱形,且
.
;
(2)当
的值为多少时,
平面
?请给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818d09d2fe7b7eff89ff0523662ed3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa34fd83a64397331db395407e12263.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56149ce7d8ec1225d2efedc06b8a3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
您最近一年使用:0次
2021-12-10更新
|
599次组卷
|
12卷引用:2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷
(已下线)2011-2012学年度广东省东山中学高二第一学期期中理科数学试卷2000年普通高等学校招生考试数学试题(广东卷)人教A版(2019) 必修第二册 过关斩将 第八章 立体几何初步 本章复习提升(已下线)6.3空间向量的应用苏教版(2019) 选修第二册 名师导学 第六章 本章复习沪教版(2020) 选修第一册 精准辅导 第3章 3.2 空间向量基本定理2000年普通高等学校招生考试数学(文)试题(新课程卷)2000年普通高等学校招生考试数学(理)试题(旧课程卷)2000年普通高等学校招生考试数学(理)试题(新课程卷)2000年普通高等学校招生考试数学(文)试题(旧课程卷)苏教版(2019)选择性必修第二册课本习题第6章复习题(已下线)考点9 垂直的判定与性质 2024届高考数学考点总动员
名校
7 . 如图,正方形
的边长为2,
的中点分别为C,
,正方形
沿着
折起形成三棱柱
,三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/566809bb-ed3c-43c5-b1bd-5b8c2c1f11b4.png?resizew=370)
(1)证明:当
时,求证:
平面
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da62d9c339d604c5ffafc82fc54e2b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62630d375713ffb142f5503340b21539.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/566809bb-ed3c-43c5-b1bd-5b8c2c1f11b4.png?resizew=370)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d06903252260d31d1a9cdeb735b089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f83464bf17f9d4d9ee6a7f299539871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
您最近一年使用:0次
2021-10-16更新
|
1108次组卷
|
3卷引用:广东省广雅中学2022届高三上学期9月月考数学试题
广东省广雅中学2022届高三上学期9月月考数学试题广东省广东广雅中学2023届高三上学期9月阶段测试数学试题(已下线)专题20 立体几何综合大题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
名校
8 . 如图,已知四棱锥
的底面
是边长为
的正方形,
,
,
是侧棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/82dc60ba-10f7-481c-98ad-3e78f4f03c68.png?resizew=191)
(1)若
为
的中点,证明
平面
;
(2)求证:不论点
在何位置,都有
;
(3)在(1)的条件下,求二面角
的大小.
![](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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618f2f945043c0fc4b2bb492206d4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2899e607479d8d1c47d954ae9ebb7144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/82dc60ba-10f7-481c-98ad-3e78f4f03c68.png?resizew=191)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求证:不论点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
(3)在(1)的条件下,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
您最近一年使用:0次
2021-08-26更新
|
261次组卷
|
2卷引用:广东省汕头市东方中学2020-2021学年高二下学期期中数学试题
名校
解题方法
9 . 在直三棱柱
中,
,点
分别是
,
的中点,
是棱
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/7a7676aa-1c2e-4a73-a0b6-5d87485c8b55.png?resizew=191)
(1)求证:
平面
;
(2)若
∥平面
,试确定
点的位置,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041c12607e485eeca0c35a80da6bf64a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c2c469e50b231ff7667fbc96c19ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094e639c2b31dc54b1b3e6456e77843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675c6e2941eecb64b358527da4d4999c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/7a7676aa-1c2e-4a73-a0b6-5d87485c8b55.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca6c8e0b690a2cdd094712c91012950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abbd58e1011307247800f094eadbc48.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54767138ed877846cec16462969fd135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在三棱柱
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ed39da4698ec7a0aa2e967501d3eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188cda17a6efcb54bffd9142b975678a.png)
,E,F分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2020/3/16/2421030489530368/2422245156036608/STEM/98619c3ec43b4c11ab2d169b40293e5e.png?resizew=247)
(1)求证:
面
;
(2)求证:
面
;
(3)在线段
上是否存在一点G,使平面
平面
,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ed39da4698ec7a0aa2e967501d3eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188cda17a6efcb54bffd9142b975678a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2239c7b9107b82024cc9e3735440f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8cbfe0f4b4ac2c137b3b146a6ebf5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2020/3/16/2421030489530368/2422245156036608/STEM/98619c3ec43b4c11ab2d169b40293e5e.png?resizew=247)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de22059d7d80f24817235269e9bb1ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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