名校
1 . 如图所示,在四棱锥
中,底面四边形
是平行四边形,且
,
,
.
平面
;
(2)当二面角
的平面角的正切值为
时,求直线BD与平面
夹角的正弦值.
![](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/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5a9a04de2ddcec2b2799ab5476f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9a336bc60a31f7bf6b92d025f79981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87aed767c861502aff771e6b0114746c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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2 . 已知在梯形
中,
//
分别是
,
上的点,
//
,沿
将梯形
翻折,使平面
平面
(如图).
平面
;
(2)求二面角
的余弦值;
(3)求点C到平面BDF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091a037987e9ac068485abee4b619a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416ac97c4e194facb7125c5779812270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d8c77f758b4a06c320be39ecb328f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febe72169c8dd4ecb57eadf7256dcbeb.png)
(3)求点C到平面BDF的距离.
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3 . 如图,已知正方体
中.F为线段
的中点,E为线段
上的动点,则下列四个结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
A.不存在点E,使![]() ![]() |
B.三棱维![]() |
C.直线![]() ![]() |
D.不存在点E,使![]() ![]() |
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名校
4 . 如图,在四棱锥
中,
平面
为等边三角形,
,点
为棱
上的动点.
平面
;
(2)当二面角
的大小为
时,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f09ad78d4eccd1a9c9ccd3c4af79c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cad98d0e4a7f999143500c62b07e6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3d2626c477fbb0b0220ccfd1eab9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689c065652544780be8b33ae92cbb6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8ef5efedfdded5f660a01f3b3f7461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
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5 . 如图,在三棱柱
中,平面
平面
,平面
平面
.
平面ABC.
(2)若
,
,求直线BC与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2623e1c4ecbd65ae5e0285c0453ffd0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba5d34d3edfc929177ef9af82d5d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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6 . 如左下图1,
是水平放置的矩形,
,将矩形
沿对角线
折起,使得平面
平面
,如右下图2.设O是
的中点,D是
的中点.
与平面
所成角的大小;
(2)连接
,设平面
与平面
的交线为直线l,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c412044acac1a6da3581ed02c979369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8520a21b909d04f763d0f61dd74bc158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c412044acac1a6da3581ed02c979369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566866c39352ba27f4179ac1f3a20c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2e4e3414aad1eba737fc135d91687.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853669d8b1f1fe103cbb35cdb94b758a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840798a31aba0783f96584e0ad7c0d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bdf1dfc5951115bc0cf7fc34add48a.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知四边形
为直角梯形,
为等腰直角三角形,平面
平面
为
的中点,
.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ebf97cae2b6ed8b10aa5d0c4a5716a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54437040defadc43560cd2ccced267bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e272f0b32fc6eaeb5955990fbe7ab0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f1bb063892dfd8f301d327e2f68feb.png)
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8 . 如图,在
中,
,
,
为
中点,沿
将
翻折至
的位置,使得平面
平面
,则三棱锥
外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa0de170250a0c8b0d23044c4c3f274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c227ba037ced067913594586d0443e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc58409e4fedf0c4782f59d176ecf8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/21/a540432e-d77d-48db-99d0-face6d914ee9.png?resizew=338)
您最近一年使用:0次
解题方法
9 . 刻画空间的弯曲性是几何研究的重要内容.用曲率刻画空间弯曲性,规定:多面体顶点的曲率等于
与多面体在该点的面角和的差(多面体的面的内角叫做多面体的面角,角度用弧度制).已知正三棱台
中,
,棱
,
的中点分别为
,
.若该棱台顶点
,
的曲率之差为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
A.![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.多面体![]() ![]() |
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名校
10 . 如图,在三棱柱
中,正方形
的棱长为2,
,点M为AB中点,
.
为直三棱柱;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c645d1dea7ca8a6eb931635dcf63d6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4149c3692068ea18563a4ef56d9d1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e363082228a653eb5b0dbc3c6161a9c9.png)
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