解题方法
1 . 如图,四棱柱
的底面
是边长为
的正方形,侧面
底面
,
,
是
的中点.
平面
;
(2)再从条件①、条件②、条件③这三个条件中选择一个 条件作为已知,使二面角
唯一确定,并求二面角
的余弦值.
条件①:
;
条件②:
;
条件③:
.
注:如果选择的条件不符合要求,第(2)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13974a1b888a77dea9bb88d354f7f511.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/2d09b1f3d1ebeae08221c210889529ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692157e4e64f78fe0d293a1c7e343ccb.png)
(2)再从条件①、条件②、条件③这三个条件中选择
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901d658f208ddea1b1aa22236a885e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901d658f208ddea1b1aa22236a885e55.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1840cdde9a6837a08a56862eaef79f.png)
条件②:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48ac2e71d3f56ad40e39ecd8dfc813c.png)
条件③:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
注:如果选择的条件不符合要求,第(2)问得0分;如果选择多个符合要求的条件分别解答,按第一个解答计分.
您最近一年使用:0次
解题方法
2 . 如图,四边形
是正方形,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5213a4756fcadb7f7f6f88420b3d5e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,
为
的中点.
(1)求证:
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
平面
;
(3)求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5213a4756fcadb7f7f6f88420b3d5e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf68a1d9aa1b647dfce4fdd778575ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/7346e3cb-e8e7-4199-83a3-d6f833b70ea9.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f392902d611863c6908a48e696e7bd8f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
3 . 如图,四棱锥
中,底面
是梯形,
,
面
,
是等腰三角形,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/5ecbc7a1-9f89-4cee-82e4-94808d144677.png?resizew=187)
(1)求证:
;
(2)设
与
所成的角为
,直线
与平面
所成的角为
,二面角
为
,从以下所给的三个条件中选出其中一个作为已知条件,求四棱锥
的体积.
①
; ②
; ③
.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee90881c743e2cff2e3128d6bdb86174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/16/5ecbc7a1-9f89-4cee-82e4-94808d144677.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829fc6685b59fdc609f32f30ebd9e6d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fe9cff5ecb699469ed2c4bbb9b584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a065865e26095d6bf74c4959dc1fef4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d058392f42ed517529d4d243937837.png)
您最近一年使用:0次
2023-04-14更新
|
1054次组卷
|
3卷引用:北京市延庆区2023届高三一模数学试题
名校
解题方法
4 . 如图,已知正方体
中,点
是棱
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
平面
;
(2)若点F是线段
的中点,求直线
与平面
所成角的正弦值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3906fd079e81869a710c9835dc8884a3.png)
(2)若点F是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3906fd079e81869a710c9835dc8884a3.png)
您最近一年使用:0次
2023-01-05更新
|
630次组卷
|
4卷引用:北京市延庆区第二中学2023-2024学年高二上学期10月质量监测数学试题
5 . 如图,在棱长为4的正方体
中,点M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/2a3964a9-c155-4f5a-b5fa-61fee5c1cd0c.png?resizew=145)
(1)求证:
平面
;
(2)求证:
;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/2a3964a9-c155-4f5a-b5fa-61fee5c1cd0c.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1496afecd92a619fbe5e9b736f06f4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5441a4e71b599d31c45940a7d2614f3.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f3750c0616ecc1d9dc8d905e26a9cc.png)
您最近一年使用:0次
名校
6 . 在四棱锥
中,
,
,
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/22/dabd7acc-d279-4ce9-b730-ea9c5f2006d6.png?resizew=161)
(1)若
是
的中点,求证:
平面
;
(2)求证:
平面
;
(3)求
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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/22/dabd7acc-d279-4ce9-b730-ea9c5f2006d6.png?resizew=161)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2022-08-21更新
|
1820次组卷
|
2卷引用:北京市延庆区2021-2022学年高二下学期期末数学试题
7 . 如图,在四棱锥
中,
平面
,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/50b24b79-520a-407f-b675-04051b9b22be.png?resizew=159)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)在棱
上是否存在点G(G与P,B不重合),使得
与平面
所成角的正弦值为
?若存在,求
的值,若不存在,说明理由.
![](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/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8248429104b06a37cd34ab341333706b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/50b24b79-520a-407f-b675-04051b9b22be.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6729fb0c5e5e9549035590144b73144.png)
您最近一年使用:0次
2023-01-05更新
|
654次组卷
|
2卷引用:北京市延庆区第二中学2023-2024学年高二上学期10月质量监测数学试题
解题方法
8 . 如图,在正方体
中,
为棱
的中点,棱
交平面
于点
.
![](https://img.xkw.com/dksih/QBM/2022/5/5/2973018637090816/2973694733713408/STEM/86d31a8e0c35471ead6e88bcfea5a911.png?resizew=161)
(1)求证:平面
平面
;
(2)求证:
;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e2c4e3e15e5b234af04535bf56bab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed31a04d1e1efb4cdcb1309bd69fb530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2022/5/5/2973018637090816/2973694733713408/STEM/86d31a8e0c35471ead6e88bcfea5a911.png?resizew=161)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549f25b5daf4dbf85bb44e274cd90fc1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2061540665f94e410177ac739e069bd6.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec91947bd89dda4ca9f74abdb1bd9ce.png)
您最近一年使用:0次
名校
9 . 如图,正方体
中,棱长为2,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/1476a87d-622e-4033-91a4-19f77dd7923d.png?resizew=159)
(Ⅰ)求证:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/1476a87d-622e-4033-91a4-19f77dd7923d.png?resizew=159)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194add18a7df1a23cf1554dc2da1b40.png)
您最近一年使用:0次
2021-08-25更新
|
554次组卷
|
4卷引用:北京市延庆区2020-2021学年高二下学期期中考试数学试题
解题方法
10 . 在四棱锥
中,
平面
,
,
,
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893833168044032/2895196300410880/STEM/5c86629b5da840feae5ba5ca075efbda.png?resizew=174)
(1)求证:
平面
;
(2)求证:
平面
;
(3)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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2e356de1dec9ce998366a1a35c0a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/227c1d105f7abf228e7a4f3097ae93f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea73441d3e6e07362ad5b35d122c0a3e.png)
![](https://img.xkw.com/dksih/QBM/2022/1/13/2893833168044032/2895196300410880/STEM/5c86629b5da840feae5ba5ca075efbda.png?resizew=174)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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