名校
解题方法
1 . 如图1,在直角梯形ABCD中,
,
,点E,F分别为边AB,CD上的点,且
.将四边形AEFD沿EF折起,如图2,使得平面
平面EBCF,点
是四边形AEFD内的动点,且直线MB与平面AEFD所成的角和直线MC与平面AEFD所成的角相等,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d15d82c67f57ed619d0911d697b5c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55bd420f7bfc74c51e7188835137750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d8c77f758b4a06c320be39ecb328f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() |
B.点![]() ![]() |
C.点![]() ![]() |
D.当点![]() ![]() ![]() |
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3卷引用:湘豫名校联考2024年2月高三第一次模拟考试数学试题
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2 . 如图所示,四棱锥
中,△
为正三角形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892076218064896/2923249386692608/STEM/f0ea3c3e6ba742ce8b31e6228523723b.png?resizew=211)
(1)求四棱锥
的体积;
(2)求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2550fca125b1f9e31f65701e4d0637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34f4a1d4e690ccc0efb3e38d8261aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490f0c21a0bfecc1447d54803af0b119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/379b96bd6556f8b3f1f6f331d24e8283.png)
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892076218064896/2923249386692608/STEM/f0ea3c3e6ba742ce8b31e6228523723b.png?resizew=211)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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3卷引用:河南省南阳市宛城区南阳市第一中学校2023届高三下学期开学考试文科数学试题
3 . 如图,在三棱柱
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/762b27ea-64a3-45ab-873e-7f8b39efaf10.png?resizew=190)
(1)证明:平面
平面
.
(2)若
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06c1cedcc4406a91783f9d37cab421e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/762b27ea-64a3-45ab-873e-7f8b39efaf10.png?resizew=190)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a269e95a9abbf6d928bfddc1466879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d808a1351940a41a2ba27ab26d7fc680.png)
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4卷引用:河南省南阳市第一中学校2021-2022学年高三上学期第五次月考数学(文)试题
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4 . 已知四棱锥
的底面
是边长为2的正方形,侧面
底面
,且
,则该四棱锥
的外接球的表面积为______ .
![](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/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7005932de8ace6e3c78a754c35466d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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