名校
解题方法
1 . 如图,在棱长为2的正方体
中,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/eec59c7f-8261-40e3-bf2c-3911f05f16f8.png?resizew=177)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/eec59c7f-8261-40e3-bf2c-3911f05f16f8.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eeb37ce111a0c102f7a5cde6875b37.png)
您最近一年使用:0次
2021-11-13更新
|
1717次组卷
|
4卷引用:福建省泉州鲤城北大培文学校2020-2021学年高二上学期期中模拟考试数学试题
名校
解题方法
2 . 如图,在四棱锥
中,
平面
,平面
平面
是正三角形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/fb94012c-41c1-4d7e-a2ed-d273c62bae9f.png?resizew=153)
(1)求证:
平面
;
(2)求证:
平面
;
(3)若
,求四面体
的体积V.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcd0a70a181f96c6b97f07720599918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90da62f1614568a0b1e5e47ea85e7e3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/fb94012c-41c1-4d7e-a2ed-d273c62bae9f.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785c7c85a503531649f9c9b4cbfcf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659b3c18ca52e5e356d8ea0fa283eaad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
您最近一年使用:0次
2021-09-18更新
|
1722次组卷
|
3卷引用:江苏省无锡市江阴市青阳中学2020-2021学年高三上学期第二次段考数学试题
2020高三·江苏·专题练习
解题方法
3 . 如图,在四棱锥P-ABCD中,底面ABCD是直角梯形,且AD∥BC,AB⊥BC,BC=2AD,已知平面PAB⊥平面ABCD,E,F分别为BC,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/c752dd6b-d635-4f34-8a55-144a142d71d0.png?resizew=131)
求证:(1)AB
平面DEF ;
(2)BC⊥平面DEF .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/c752dd6b-d635-4f34-8a55-144a142d71d0.png?resizew=131)
求证:(1)AB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)BC⊥平面DEF .
您最近一年使用:0次
名校
解题方法
4 . 如图,在正方体ABCDA1B1C1D1中,E,F,G,H分别是BC,CC1,C1D1,A1A的中点.求证: EG∥平面BB1D1D.
![](https://img.xkw.com/dksih/QBM/2021/3/18/2680420021272576/2684993440227328/STEM/08ab0e6fa8af4bd7b512fe65ff8dfe90.png?resizew=124)
您最近一年使用:0次
名校
5 . 已知斜三棱柱
的侧面
与底面
垂直,
.且
为
中点,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/2021/3/4/2670588615450624/2670841255002112/STEM/b56a43efd2354b8daadc949665b5183f.png?resizew=172)
(1)求证:
平面
;
(2)求直线
与底面
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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bddea1644933eb8ca4dc980931417d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2021/3/4/2670588615450624/2670841255002112/STEM/b56a43efd2354b8daadc949665b5183f.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6748d9b9948485c5ba87ca8751c6e053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4c87f4da030d05da7c0fa59384743e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2021-03-04更新
|
2599次组卷
|
5卷引用:江苏省苏州市工业园区园区三中2019-2020学年高一下学期期中数学试题
江苏省苏州市工业园区园区三中2019-2020学年高一下学期期中数学试题(已下线)8.6空间直线、平面的垂直(2)(精炼)-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)吉林省白城市第一中学2020-2021学年高一下学期期中数学试题黑龙江省嫩江市第一中学校等五校2020-2021学年高一下学期期末考试数学试题江西省南昌市进贤县第一中学2020-2021学年高二下学期期中考试数学(文)试题
名校
解题方法
6 . 如图,在三棱锥
中,点
分别是
的中点,
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634710018048000/2635906144518144/STEM/6c7321b9-d1d0-4625-9f78-c00380456784.png)
(1)证明:
∥平面
;
(2)若三棱锥
是底边长为3的正三棱锥,且该体积与表面积为24的正方体的体积相等,求该正三棱锥的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://img.xkw.com/dksih/QBM/2021/1/12/2634710018048000/2635906144518144/STEM/6c7321b9-d1d0-4625-9f78-c00380456784.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
您最近一年使用:0次
2021-01-14更新
|
709次组卷
|
4卷引用:海南省海口市琼山中学2019-2020学年度高一年级下学期期中考试数学科试题
名校
解题方法
7 . 矩形ABCD中,
,P为线段DC的中点,将
沿AP折起,使得
.
![](https://img.xkw.com/dksih/QBM/2020/12/27/2623074517852160/2623475375554560/STEM/26efc6e6-1f8c-4696-8bef-71777ab3d430.png)
(1)若E为BD的中点,证明:
平面ADP;
(2)证明:平面
平面ABCP.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4e4a162f12d12a082b8d8fdd1aeab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9953b7b5c647641edbec4c2ab90a65f4.png)
![](https://img.xkw.com/dksih/QBM/2020/12/27/2623074517852160/2623475375554560/STEM/26efc6e6-1f8c-4696-8bef-71777ab3d430.png)
(1)若E为BD的中点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b77a5c3865855fbb3d24f9522ced8d.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,在直三棱柱
中,
,
,
,
,
为线段
的中点,
为线段
的中点,
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2020/12/14/2614108788490240/2614812321808384/STEM/7aac68f56a5b43859f50f54c3dff63bb.png?resizew=176)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d0fdc5a00ca0e857b89a7e1420df29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/2020/12/14/2614108788490240/2614812321808384/STEM/7aac68f56a5b43859f50f54c3dff63bb.png?resizew=176)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1847074419e82f9f04b9596e4fbe19.png)
您最近一年使用:0次
2020-12-15更新
|
2305次组卷
|
5卷引用:吉林省通榆县第一中学2020-2021学年高三上学期期中考试数学(文)试题
吉林省通榆县第一中学2020-2021学年高三上学期期中考试数学(文)试题(已下线)第八单元 立体几何(B卷 滚动提升检测)-2021年高考数学(文)一轮复习单元滚动双测卷内蒙古赤峰二中2020-2021学年高二上学期第二次月考数学(文)试题陕西省宝鸡市陈仓区2021届高三下学期教学质量检测(二)文科数学试题浙江省台州市天台中学2021-2022学年高二上学期返校考试数学试题
9 . 如图,在三棱柱
中,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcca4982eda404a0cd8193e35a5be6b2.png)
,
分别是
的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/007f2429-49cb-472e-a801-17e7c8adcbb9.png?resizew=147)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcca4982eda404a0cd8193e35a5be6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450176ba93397527fc3520c55dd1476a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/007f2429-49cb-472e-a801-17e7c8adcbb9.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92bced6bf70db7229db85f2b10339431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
您最近一年使用:0次
2020-12-05更新
|
1235次组卷
|
3卷引用:广东省紫金县中山高级中学2020-2021学年高二上学期期中数学试题
10 . 如图,四面体ABCD中,点E,F分别为线段AC,AD的中点,平面
平面
,
,
,垂足为H.
![](https://img.xkw.com/dksih/QBM/2020/11/18/2595204682768384/2601979299405824/STEM/a02fff92-5ea3-4f41-8c97-80ec262792ac.png)
(1)求证:
;
(2)求证:平面
平面ABC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7898ccc0ec40a1460fae5b5bf6bc001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddb409de7d8056cdef2cd68080fe47ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7903326ef7b584fb53651194b7541fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a7cf70f8772d8fea4599b18df2c88f.png)
![](https://img.xkw.com/dksih/QBM/2020/11/18/2595204682768384/2601979299405824/STEM/a02fff92-5ea3-4f41-8c97-80ec262792ac.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf85bbbf81e16ba6da39bfebf0e09a7.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d443d65476dd21c8e1f9345b3f13439e.png)
您最近一年使用:0次
2020-11-27更新
|
2640次组卷
|
6卷引用:四川省蓉城名校联盟2020-2021学年高二第一学期期中联考理科数学试题
四川省蓉城名校联盟2020-2021学年高二第一学期期中联考理科数学试题四川省成都市蓉城名校联盟2020-2021学年高二(高中2019级)上学期期中联考文科数学试题(已下线)第二章+点、直线、平面之间的位置关系(能力提升)-2020-2021学年高一数学单元测试定心卷(人教版必修2)四川省内江市第六中学2020-2021学年高二上学期第三次月考数学理科试题四川省内江市第六中学2020-2021学年高二上学期第三次月考数学文科试题四川省成都市2020-2021学年高二上学期期中数学理科试题