解题方法
1 . 已知直线
,平面
,
,以下的真命题是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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2 . 如图,四棱锥P﹣ABCD的底面是梯形.BC∥AD,AB=BC=CD=1,AD=2,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8f9efada515904b015baa8e2fc1b8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/bd80ff47-3d74-46af-9200-fe32847a61d5.png?resizew=177)
(Ⅰ)证明;AC⊥BP;
(Ⅱ)求直线AD与平面APC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96ac79190e1b93c16b5d00a1b516281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8f9efada515904b015baa8e2fc1b8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/bd80ff47-3d74-46af-9200-fe32847a61d5.png?resizew=177)
(Ⅰ)证明;AC⊥BP;
(Ⅱ)求直线AD与平面APC所成角的正弦值.
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2020-03-22更新
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7卷引用:2020届浙江省杭州二中高三上学期返校考试数学试题
2020届浙江省杭州二中高三上学期返校考试数学试题2020届浙江省温州中学高三下学期3月高考模拟测试数学试题福建省三明市2019-2020学年普通高中高三毕业班质量检查A卷(5月联考)理科数学试题福建省三明市2019-2020学年高三(5月份)高考(理科)数学模拟试题(已下线)考点23 运用空间向量解决立体几何问题-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)(已下线)专题19 立体几何综合-2020年高考数学母题题源全揭秘(浙江专版)安徽省滁州市定远县第二中学2022届高三下学期高考模拟检测理科数学试题
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解题方法
3 . 一个几何体的三视图如图所示,其中俯视图为正方形,则该几何体的侧面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f3b91b89-aea1-4c36-b4fa-e8a598fed968.png?resizew=250)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/f3b91b89-aea1-4c36-b4fa-e8a598fed968.png?resizew=250)
A.![]() | B.![]() | C.![]() | D.6 |
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解题方法
4 . 如图,在几何体
中,四边形
为菱形,且
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/d92d609b-6d32-4e50-9364-38b91fed2b41.png?resizew=239)
(1)求证:平面
平面
;
(2)
为
中点,当
,
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2622edcd2b9e514734ded7fbec3f7c6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/d92d609b-6d32-4e50-9364-38b91fed2b41.png?resizew=239)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803e96e7ccd7a84c1d87c394f271223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfe0538ece1daca775b1c0d3fad69d4.png)
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2020-03-22更新
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3卷引用:2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题
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解题方法
5 . 过点
作抛物线
的两条切线
,
,设
,
与
轴分别交于点
,
,则
的外接圆方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01141f06fd94cf14ee578cbbdb38a79a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 如图①,△ABC是以AC为斜边的等腰直角三角形,△BCD是等边三角形.如图②,将△BCD沿BC折起,使平面BCD⊥平面ABC,记BC的中点为E,BD的中点为M,点F、N在棱AC上,且AF=3CF,C
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4a4865e3-ed0e-4387-b7a7-f80e5bf2b328.png?resizew=456)
(1)试过直线MN作一平面,使它与平面DEF平行,并加以证明;
(2)记(1)中所作的平面为α,求平面α与平面BMN所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d045828938cfce8f0ec3b8f1f9dfc6de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/4a4865e3-ed0e-4387-b7a7-f80e5bf2b328.png?resizew=456)
(1)试过直线MN作一平面,使它与平面DEF平行,并加以证明;
(2)记(1)中所作的平面为α,求平面α与平面BMN所成锐二面角的余弦值.
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7 . 已知某几何体由一个四棱锥和一个半圆柱组成,其三视图如图所示,则该几何体的表面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc488a51-c510-46bb-a98b-2e479fbbf0bc.png?resizew=117)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/dc488a51-c510-46bb-a98b-2e479fbbf0bc.png?resizew=117)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 已知
、
是异面直线,给出下列结论:
①一定存在平面
,使直线
平面
,直线
平面
;
②一定存在平面
,使直线
平面
,直线
平面
;
③一定存在无数个平面
,使直线
与平面
交于一个定点,且直线
平面
.
则所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
①一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe623bd25476a860fa4c2a179b81464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②一定存在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764b59b077bda19d131095b454942d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
③一定存在无数个平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
则所有正确结论的序号为( )
A.①② | B.② | C.②③ | D.③ |
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2020-03-21更新
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448次组卷
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3卷引用:【全国市级联考】北京市西城区2017-2018学年高一下学期期末考试数学试题
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解题方法
9 . 已知三棱柱
的底面是正三角形,侧面
为菱形,且
,平面
平面
,
、
分别是
、
的中点.
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
平面
;
(2)求证:
;
(3)求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2020/3/19/2423138566766592/2423630358208512/STEM/05a2608adae7431da5b603bf448c3633.png?resizew=217)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb9aa113258bfa138c95a621f64fc74.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
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2020-03-20更新
|
664次组卷
|
4卷引用:【全国百强校】天津市静海县第一中学2017-2018学年高一下学期期中考试数学试题
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解题方法
10 . 如图,在三棱锥
中,
平面
,
,
分别为棱
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/c086d471-6389-479b-9c2a-5fb8e02b812e.png?resizew=196)
(1)求证:
;
(2)当
时,求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46cf65da6cf1a1a7fc5c9c01bdd83a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6476880c8c4a6a9c1883d6fbb42cd33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534c25b4b9ff9aa0cf6c05ae3a8f02f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/c086d471-6389-479b-9c2a-5fb8e02b812e.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01071e7ea0fe51f5d9912c27343db0ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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2卷引用:2020届安徽省安庆二、七中高三开学考试数学(理)试题