如图所示,已知两个正方形
和
不在同一平面内,
,
分别为
,
的中点.若
,平面
⊥平面
,则线段
的长为_____ ,线段
的长为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.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/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/13e68b26-8fe7-4204-a189-2589965b20ae.png?resizew=124)
更新时间:2023-04-19 16:15:42
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解题方法
【推荐1】已知
在平面
内,
,
平面
,则直线BA与DC的位置关系是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a7504eab46f415daeab05272316cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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【推荐2】设
和
都是平面
的垂线,其垂足分别为
.已知
,那么线段![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64dee37c8821865a3d13fbfcd9dac7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
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真题
【推荐1】已知平面
,P是空间一点,且P到
的距离分别是1、2,则点P到l的距离为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8a1d1c06fb34527b3f09a150805ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
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【推荐2】将边长为1的正方形
中,把
沿对角线AC折起到
,使平面
⊥平面ABC,则三棱锥
的体积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f931eacfa227d887b0f4665fde5e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7f100848814c3e187f2d5ad7980ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
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【推荐3】平面角是直角的二面角称为__________ ,此时两个平面
互相垂直,记为__________ .
平面与平面垂直的判定定理
文字语言:如果一个平面过另一个平面的__________ ,那么__________ .
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/eb5d5a29-dd94-48af-8699-d1fe1d34dd6c.png?resizew=144)
符号语言:若
,则__________ .
平面与平面垂直的性质定理
文字语言:两个平面垂直,如果一个平面内有一条直线__________ ,那么这条直线__________ .
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/8d032bee-f13e-45e8-a7fd-79cfab937c96.png?resizew=144)
符号语言:若
,则__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
平面与平面垂直的判定定理
文字语言:如果一个平面过另一个平面的
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/eb5d5a29-dd94-48af-8699-d1fe1d34dd6c.png?resizew=144)
符号语言:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fa261aa9283f16a4e67614350c552d.png)
平面与平面垂直的性质定理
文字语言:两个平面垂直,如果一个平面内有一条直线
图形语言:如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/8d032bee-f13e-45e8-a7fd-79cfab937c96.png?resizew=144)
符号语言:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd921fc1e0f77d7075a0a23cbc661a0.png)
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