名校
1 . 化学中经常碰到正八面体结构(正八面体是每个面都是正三角形的八面体),如六氟化硫(化学式
)、金刚石等的分子结构.将一个正方体六个面的中心连线可得到一个正八面体
(如图),已知正方体棱长为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f78965316691f13f50ace39a5edd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94db528f0e99604cac52a2d82b7d9146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
A.正八面体![]() ![]() |
B.正八面体![]() ![]() |
C.若点P为棱EB上的动点,则三棱锥![]() ![]() |
D.若点P为棱EB上的动点(包括端点),则直线CP与平面GHMN所成角的正弦值的取值范围是![]() |
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解题方法
2 . 如图,棱长为2的正方体
中,
为棱
的中点,
为正方形
内一个动点(包括边界),且
∥平面
,则下列说法正确的有( )
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a73120cd0988eb4a63436e7a4b9470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
A.记![]() ![]() ![]() ![]() ![]() ![]() |
B.动点![]() ![]() |
C.三棱锥![]() ![]() |
D.当三棱锥![]() ![]() |
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3 . 如图,在直三棱柱
中,
,
,
,
是边
的中点,过点A,B,D作截面交
于点E,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef8866ccf160ddc441bf69c5d3a3d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
A.![]() | B.平面![]() ![]() |
C.![]() ![]() | D.点![]() ![]() ![]() |
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4 . 平行四边形ABCD中
,且
,AB、CD的中点分别为E、F,将
沿DE向上翻折得到
,使P在面BCDE上的投影在四边形BCDE内,且P到面BCDE的距离为
,连接PC、PF、EF、PB,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
A.![]() |
B.![]() |
C.三棱锥![]() ![]() |
D.点Q在线段PE上运动,则![]() ![]() |
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解题方法
5 . “阿基米德多面体”也称为半正多面体,它是以边数不全相同的正多边形为面的多面体,体现了数学的对称美.将一个棱长为2的正方体沿交于一顶点的三条棱的中点截去一个三棱锥,共要截去八个三棱锥,形成一个由正三角形和正方形围成的“阿基米德多面体”,如图,则( )
A.该多面体共有12个顶点,14个面 |
B.该多面体的表面积为![]() |
C.该多面体的外接球体积为![]() |
D.所在直线与直线![]() ![]() |
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解题方法
6 . 已知平面
平面
,
,点
,
,若直线
,直线
,直线
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa807136194c18d3ac58902c67f9333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b707f5ee4fbb2e637c65fbc6d8ed03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0b6de90bb936cdb09629123100145d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4f3a6e86e58e9a5cd2f2dfdea2b08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09642d9d26684a580d2727b46728422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af680499446f4f2cd3c3d6cb37905efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb088614157a85ed7cb11802e49a2981.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
7 . 如图,三棱锥
C中,PA,PB,PC两两垂直,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2aaed1e9ead175f30f7130569d0411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbda0c56ebe2562f4c341c58126bc311.png)
A.![]() |
B.三棱锥![]() ![]() |
C.点P到平面ABC的距离为![]() |
D.三棱锥![]() ![]() |
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解题方法
8 . 如图,在正方体
中,
为棱
上的动点,
平面
为垂足,下列结论正确的是( )
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e0bd4b30dc777ac9da80f6baa3eb31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b7e86d73300e4b2cb5a2138997a6ca.png)
A.![]() |
B.三棱锥![]() |
C.![]() |
D.![]() ![]() ![]() |
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解题方法
9 . 如图,在三棱柱
中,已知点
分别在
上,且
经过
的重心,点
分别是
的中点,且
四点共面,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb1884afa6b9d2625b489d6a0b4667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ea060a38d34288db2b99ab280acd6e.png)
A.![]() |
B.![]() ![]() |
C.![]() |
D.棱柱被平面![]() ![]() ![]() ![]() |
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10 . 已知
是两条不同的直线,
是平面,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,则
的关系可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd089bc2a70824f3c223b459490054e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
A.平行 | B.垂直 | C.相交 | D.异面 |
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