解题方法
1 . 如图,几何体
为直四棱柱
截去一个角所得,四边形
是菱形,
,点
为棱
的中点.
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52eab6de89f4d4e69650e94e0968744.png)
![](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/4ecc33c358ffa4fee3a57dd3468065f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611db7041a52b0c0967a2e6f7577285c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e2c643dd6501b20c46c5c6527a2634.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0de3aeeff0480033ffd050165baf82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
您最近一年使用:0次
2024-05-23更新
|
534次组卷
|
3卷引用:海南省2022届高三高考全真模拟卷(四)数学试题
解题方法
2 . 如图,在直三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/7acca537-f112-4f2c-8ebe-4b52c2a2b724.png?resizew=124)
(1)求证:平面
平面SAB;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8af8eab56cb1e747e4a713d0e105ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5ba170e666d7228ca08644a4f94d94.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/9/7acca537-f112-4f2c-8ebe-4b52c2a2b724.png?resizew=124)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6e6192cf24ada791c26c2d6d434069.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8f249c2bec5e988d4b1d233c80c5b4.png)
您最近一年使用:0次
解题方法
3 . 如图,在多面体
中,
,四边形
是正方形,四边形
是矩形,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/f110bfe8-d7c4-44c7-8ff3-a69430bbd4d5.png?resizew=138)
(1)证明:平面
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1c122603b60b6f1a1334ddb56c3fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70bcab5b71aad0a849018c5884c6391a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/f110bfe8-d7c4-44c7-8ff3-a69430bbd4d5.png?resizew=138)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
您最近一年使用:0次
4 . 已知四棱锥
的底面为正方形,其中点
在平面
上的投影为
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/bc6163fd-1ba4-4af7-8bfb-651b1b5f2075.png?resizew=142)
(1)求证:平面
平面
;
(2)若
与平面
所成角为45°,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/bc6163fd-1ba4-4af7-8bfb-651b1b5f2075.png?resizew=142)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9332d230f25309248ff2a6161f060229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd55674bc07e964ed6367e73b6f92ff1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b937f48e47ea687e0d87297fba5cdc5b.png)
您最近一年使用:0次
解题方法
5 . 如图,在平行四边形
中,
是
上靠近点
的三等分点,过点
作
,分别交
,
于点
,
,将
沿
折起至
.
,求证:平面
平面
;
(2)若
在线段
上,当
为何位置时,
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5486478d317b66a6830138d6e87f752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164a4df60a15587971e883cf557b5ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f45daa08d8d7105dc9bad40f7c7a745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d3a3f9bae62377ff6e18e7d94e21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/124e1461a6c8df9f47bca2f1dc1352f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
解题方法
6 . 如图,梯形
中,
,
,将
沿对角线
折起.设折起后点A的位置为
,且平面
平面
.给出下面四个命题:
①
;②三棱锥
的体积为
;③
平面
;④平面
平面
.其中正确命题的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/1631ca8a-57b4-4a5c-866b-123c5fb4be9d.png?resizew=315)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b57d396378da35e8b2bb3882751db8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386c7de62e8f9a8161ebaefe6b4ec35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe052786101dfcc941480919eb2cecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1056ae5ef77fcabea2e076e271cd72ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d138354c4e021ac8ae2a2fb176ca14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8c968d4a1798957d5134b45f5049d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/1631ca8a-57b4-4a5c-866b-123c5fb4be9d.png?resizew=315)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
7 . 在四棱锥
中,
平面
为等腰直角三角形,底面
为平行四边形,且
是线段
的中点,F在线段
上运动,记
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/2578f09a-a901-466d-9d4c-8fe61323e01a.png?resizew=168)
(1)若
,求证:平面
平面
;
(2)若
,求三棱锥
的体积.
![](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/3bcd0a70a181f96c6b97f07720599918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f4e3f9d2fb9926ac1f1843535adec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b597ab26acac3a6633151f4e59bda4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/2578f09a-a901-466d-9d4c-8fe61323e01a.png?resizew=168)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758e71a79a3741be75d7a856202e0f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f5b538bcfb898fcc9d3a2dd8a1b080.png)
您最近一年使用:0次
解题方法
8 . 如图,在四棱锥
中,四边形
为菱形,
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/40d84563-528a-444d-b5c8-e84f63647931.png?resizew=157)
(1)求证:平面
平面
;
(2)若
,二面角
的正切值为2,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26745d0bbcb639f5425083ce1e7f4695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/25/40d84563-528a-444d-b5c8-e84f63647931.png?resizew=157)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368eebcb7b3b3c5c5af72f83e13867df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ab41769d8021bc324a9cd7913baa5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ab58222b40ffaf2dd6a66a81806e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
您最近一年使用:0次
解题方法
9 . 如图,在四棱锥
中,底面
是矩形,平面
⊥平面
,
为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/aa208230-f1d8-4e11-8ea4-37f5ac0a338f.png?resizew=158)
(1)求证: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/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b8e42d656d2da9ecf96ac60b6f99c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db86a481972bd2dc553889617002d146.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/aa208230-f1d8-4e11-8ea4-37f5ac0a338f.png?resizew=158)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87136d5f4908fa04dd99bc35a16f393.png)
您最近一年使用:0次
解题方法
10 . 已知直三棱柱
的底面为正三角形,
是侧棱
上一点,且
,则三棱锥
外接球的体积为_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8fed0e9b4027890a0cc13d51253d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9499f0e312799d87f5377f30565abc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc27121b923731da934338667acd1e6c.png)
您最近一年使用:0次