名校
解题方法
1 . 已知平面四边形
由等腰
和
组成,
,O为
上的点且
(如图1所示),将等腰
沿
折起,点M折至点D位置,使得平面
平面
(如图2所示).
![](https://img.xkw.com/dksih/QBM/2022/3/12/2934854783303680/2936637418496000/STEM/876eda98-db62-4b49-b468-57dfbb106600.png?resizew=258)
(1)求证:
;
(2)若点E在棱
上,且满足
,平面
和平面
所成锐二面角的余弦值为
,求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40c49d6e2fc6fbdc21ff61841b586a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b55c9dfab957f3011f8342cdc58d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6647249712de84b706b773e8f752d442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40c49d6e2fc6fbdc21ff61841b586a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2022/3/12/2934854783303680/2936637418496000/STEM/876eda98-db62-4b49-b468-57dfbb106600.png?resizew=258)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad3016034d5b567427c9dcf8edaea9.png)
(2)若点E在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e7b83a2497d1662d1a95ec4cbb7495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-03-15更新
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857次组卷
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2卷引用:宁夏银川市六盘山高级中学2023届高三三模数学(理)试题