1 . 如图,四棱锥
中,面
面
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/3029c473-a9ca-4c73-b72c-1a1c1552b390.png?resizew=200)
(1)证明:
;
(2)求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641aa755ada1d83daafc82d5f1fa88db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf198283a5ce91e6eb2bca3f116a972c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3c34fe8c99745f61e57db23bbdb1e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/3029c473-a9ca-4c73-b72c-1a1c1552b390.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2020-10-16更新
|
820次组卷
|
2卷引用:浙江省浙南名校联盟2020-2021学年高三上学期第一次联考数学试题
名校
2 . 如图,在四棱锥
中,
平面
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4b6176de-f6cf-4b53-84a3-d7a53edd7e04.png?resizew=160)
(1)求证:
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f776c501a180174257d5dff5ed599907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4b6176de-f6cf-4b53-84a3-d7a53edd7e04.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef67284b03310b208a185cc6a86d5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb5255e2159617505e0c87d01437a57.png)
您最近一年使用:0次
2020-05-25更新
|
261次组卷
|
2卷引用:2020届湖北省武汉市部分学校高三下学期5月在线学习摸底检测理科数学试题
名校
3 . 已知如图一
,
,
,
,
分别为
,
的中点,
在
上,且
,
为
中点,将
沿
折起,
沿
折起,使得
,
重合于一点(如图二),设为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/46b8dd19-1f97-4ef1-a34e-9ac41298b41c.png?resizew=280)
(1)求证:
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08313da7b66283d2e0b3987f3e6761f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4f947e0f238c37854afa0bf6b93a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.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/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/46b8dd19-1f97-4ef1-a34e-9ac41298b41c.png?resizew=280)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0df73a49d4348a5c1e3aaa149cc8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbbe7f48676298f2ee0cb1901992eaf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c19de14651645718682d3d2af5993b0.png)
您最近一年使用:0次
名校
4 . 如图,在四棱柱
中,底面ABCD是等腰梯形,
,
,
,顶点
在底面ABCD内的射影恰为点C.
![](https://img.xkw.com/dksih/QBM/2020/3/24/2426683543445504/2426969450962944/STEM/449b5ed97f83408886aba846afb04e0a.png?resizew=198)
(1)求证:BC⊥平面ACD1;
(2)若直线DD1与底面ABCD所成的角为
,求平面
与平面ABCD所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://img.xkw.com/dksih/QBM/2020/3/24/2426683543445504/2426969450962944/STEM/449b5ed97f83408886aba846afb04e0a.png?resizew=198)
(1)求证:BC⊥平面ACD1;
(2)若直线DD1与底面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
您最近一年使用:0次
2020-03-25更新
|
288次组卷
|
4卷引用:湖北省孝感市应城市第一高级中学2019-2020学年高二下学期期中数学试题
名校
5 . 如图,在三棱柱
中,侧面
是边长为4的菱形,且
,面
面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/425b9792-45ee-4115-8a16-27240fb0b943.png?resizew=207)
(1)求证:
面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecf0d955692e3ddacbda6035c70a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6fbf78350d99b5310b3d824d6d0943.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/425b9792-45ee-4115-8a16-27240fb0b943.png?resizew=207)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91441b6a208013fa5e8ddf7c8cd1f43d.png)
您最近一年使用:0次
2020-06-03更新
|
379次组卷
|
2卷引用:2020届湖北省武汉市高三下学期5月质量检测理科数学试题
6 . 如图,在四棱台ABCD-A1B1C1D1中,底面ABCD是菱形,∠ABC=
,∠B1BD=
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58df8d911935cca1738567b656c8e3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41430e9e5f22c2330333613390612fb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/4ee63947-6239-496a-88ad-5660c468f68e.png?resizew=179)
(1)求证:直线AC⊥平面BDB1;
(2)求直线A1B1与平面ACC1所成角的正弦值.
您最近一年使用:0次
2020-03-19更新
|
5194次组卷
|
10卷引用:2020届浙江省名校协作体高三下学期3月第二次联考数学试题
2020届浙江省名校协作体高三下学期3月第二次联考数学试题安徽省合肥一中2020-2021学年高二上学期10月段考数学(理)试题湖北省九校教研协作体2022-2023学年高二上学期9月联考数学试题湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题山东省齐鲁2021-2022学年3月份高一阶段性质量检测试卷A福建省福州格致中学2022届高三数学模拟试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-2广东省中山市2023-2024学年高二上学期期末统一考试数学试题2024年全国普通高中九省联考仿真模拟数学试题(三)湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题
名校
7 . 如图,四棱锥
中,
平面ABCD,底面ABCD是正方形,
,E为PC上一点,当F为DC的中点时,EF平行于平面PAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f62a42fc-8213-4202-b2e2-53e2ff927791.png?resizew=180)
(Ⅰ)求证:
平面PCB;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99926bf272cd757f0985c69b390ebcce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f62a42fc-8213-4202-b2e2-53e2ff927791.png?resizew=180)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eaa13915786802de6a540d56dec821b.png)
您最近一年使用:0次
2020-02-10更新
|
418次组卷
|
4卷引用:2020届湖北省部分重点中学高三第二次联考数学试卷理科试题
2020届湖北省部分重点中学高三第二次联考数学试卷理科试题重庆市第一中学2019-2020学年高二下学期期中数学试题(已下线)数学-6月大数据精选模拟卷02(山东卷)(满分冲刺篇)重庆市凤鸣山中学2020-2021学年高二下学期期中数学试题
8 . 如图,三棱柱
中,
侧面
,已知
,
,
,点E是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/1941582f-9b4b-402d-a854-595f38408e1a.png?resizew=163)
(1)求证:
平面ABC;
(2)在棱CA上是否存在一点M,使得EM与平面
所成角的正弦值为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec738fd1916032dff2b93f84f039404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7932b50fa677dfcd8e3b5061a90c133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/1941582f-9b4b-402d-a854-595f38408e1a.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ad7c180d6d084ecb25f23cb6fe9b10.png)
(2)在棱CA上是否存在一点M,使得EM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d46f7e72b55d2ff3d9bc38e02b31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0f4f8e3032f67e672b63791cc4d9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7e6f1b753b73381b71eb5f8cc7da42.png)
您最近一年使用:0次
2020-03-10更新
|
1318次组卷
|
13卷引用:2020届广东省广州市执信中学高三2月月考数学(理)试题
2020届广东省广州市执信中学高三2月月考数学(理)试题2020届山东省济宁市嘉祥一中高三下学期第一次质量检测数学试题2020届陕西省西安市西北工业大学附中高三下学期4月适应性测试数学(理)试题四川省射洪中学校2020-2021学年高二上学期第三次月考数学(理)试题黑龙江省哈尔滨市第六中学2021届高三12月月考数学(理)试题广东省广州市执信中学2021届高三上学期第四次月考数学试题湖北省武汉市部分重点中学2021-2022学年高二上学期期中联考数学试题湖北省武汉市华中科技大学附属中学2022-2023学年高二上学期9月月考数学试题广东省深圳市盐田区深圳外国语学校2021届高三上学期1月月考数学试题重庆实验外国语学校2020-2021学年高二下学期6月月考数学试题甘肃省嘉陵关市第一中学2020-2021学年高三下学期四模考试数学(理)试题贵州省毕节市第一中学2021-2022学年高二上学期第二次阶段性考试数学(理)试题江苏省连云港市赣榆智贤中学2022-2023学年高二下学期3月学情检测数学试题
9 . 如图,在四棱锥S﹣ABCD中,侧面SCD为钝角三角形且垂直于底面ABCD,
,点M是SA的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/0b1d512a-660b-4937-b414-a678c2564ff6.png?resizew=187)
(1)求证:
平面SCD;
(2)若直线SD与底面ABCD所成的角为
,求平面MBD与平面SBC所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7812ef34a2b02f9ce73952d5db2eee35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0254c51c4e3e5ca7190cb4cd97defbb5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/0b1d512a-660b-4937-b414-a678c2564ff6.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
(2)若直线SD与底面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
您最近一年使用:0次
2020-05-07更新
|
198次组卷
|
2卷引用:2020届湖北省高三下学期4月高考模拟理科数学试题
名校
10 . 在平行四边形
中,
,
,
,
是EA的中点(如图1),将
沿CD折起到图2中
的位置,得到四棱锥是
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453971677822976/2454901004050432/STEM/d5058c8c-a54b-40f9-9c97-196fb71047c7.png)
(1)求证:
平面PDA;
(2)若PD与平面ABCD所成的角为
.且
为锐角三角形,求平面PAD和平面PBC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb5d56b5ef73dc6046f1a11e1e18919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2761cf826c9f9850fb93071971a17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a05d97047e3a5c8e125d334d478ee8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6414089941feb5d8a4a6a49566b9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b265d121f9ebc13671a5719604476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453971677822976/2454901004050432/STEM/d5058c8c-a54b-40f9-9c97-196fb71047c7.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)若PD与平面ABCD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8fe4026f1a0745ab9aa9fe64f0e482.png)
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2020-05-03更新
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