如图,在四棱锥P-ABCD中,底面ABCD是平行四边形,PA⊥平面ABCD,E是BC的中点,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/22/2899878736248832/2943331681943552/STEM/628775cec23d45eca34d901462079610.png?resizew=255)
(1)证明:
;
(2)求平面PAB与平面PDE的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://img.xkw.com/dksih/QBM/2022/1/22/2899878736248832/2943331681943552/STEM/628775cec23d45eca34d901462079610.png?resizew=255)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f343971a5a48113e877a056ed6b6d608.png)
(2)求平面PAB与平面PDE的夹角的大小.
更新时间:2022-03-24 21:26:32
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解答题-证明题
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解题方法
【推荐1】如图所示,正方形ABCD和矩形ACEF所在的平面相互垂直,已知AB=2,
.
(I)求证:EO⊥平面BDF;
(II)求二面角A﹣DF﹣B的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1724da306480348f03f4ea0a66bd9ec3.png)
(I)求证:EO⊥平面BDF;
(II)求二面角A﹣DF﹣B的大小.
![](https://img.xkw.com/dksih/QBM/2011/3/4/1570025485230080/1570025490292736/STEM/457624fd605e4db4ab4c49ccc29a012e.png?resizew=232)
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【推荐2】如图所示,在棱长为2的正方体
中,
、
分别为
、
的中点.
(Ⅰ)求证:
//平面
;
(Ⅱ)求证:
;
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
![](https://img.xkw.com/dksih/QBM/2012/2/17/1570744981004288/1570744986304512/STEM/d5f71ea2-bc73-4b2c-b2c8-9b82da5fd984.png?resizew=170)
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解答题-证明题
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【推荐1】在如图所示的多面体MNABCD中,四边形ABCD是边长为
的正方形,其对角线的交点为Q,
平面ABCD,
,
,点P是棱DM 的中点.
(1)求证:
;
(2)求直线CN和平面AMN所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa15f54378bb35cc97a55f6cf0df1f6.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/22/59dbb347-efcc-4153-bd77-82b09489e332.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b154270249b0ef54ddb26137b2681a.png)
(2)求直线CN和平面AMN所成角的正弦值.
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解题方法
【推荐2】已知平行四边形
中,
,
为
的中点,且△
是等边三角形,沿
把△
折起至
的位置,使得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/c9b065d2-b13d-4b26-b990-128258088629.png?resizew=257)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/7ab73ea2-efec-4917-a379-c651c780764b.png?resizew=241)
(1)
是线段
的中点,求证:
平面
;
(2)求证:
;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502fc5e3c7f636aac9064ec69018c95c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/c9b065d2-b13d-4b26-b990-128258088629.png?resizew=257)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/8/7ab73ea2-efec-4917-a379-c651c780764b.png?resizew=241)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf93370d9638286955c65203ce50ff1.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
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解答题-证明题
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【推荐3】如图,在正方体
中,棱长为1,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/2021/7/7/2759178987642880/2778935371702272/STEM/e33a6177-21b2-47e1-8127-47398d3a1e39.png?resizew=267)
(1)求证:
平面
;
(2)求证:
平面
;
(3)求三棱锥
的体积.
![](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/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://img.xkw.com/dksih/QBM/2021/7/7/2759178987642880/2778935371702272/STEM/e33a6177-21b2-47e1-8127-47398d3a1e39.png?resizew=267)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96946eaa2878fb8433eb2a97797a32b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5074d7e735ef0b311c79cd86bada4ac.png)
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【推荐1】如图,已知矩形
所在平面与平面
垂直,在直角梯形
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/33c99ddc-673e-48e7-8d41-ad78000f6a82.png?resizew=168)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb55b4b96849ab53b0cb97332801b86d.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/33c99ddc-673e-48e7-8d41-ad78000f6a82.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9ee68a3fdc62a86e53d4048e8fc04e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/335187895f612ce811414cfbedf89467.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd6a2215f47cdb01078326d245b1523.png)
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解答题-作图题
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解题方法
【推荐2】在正方体
中,
分别是棱
和
上异于端点的动点,将经过三点
的平面被正方体截得的图形记为
.如图中
时截面图形
为矩形.
(1)在图中作出截面图形
为梯形的情形;(直接画出图形即可,不需说明)
(2)当点
为
中点时,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d04ea588f556c3b874b7e68ea69f49e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/29/5db5de67-b86d-4aaf-b4be-12f24a3ef879.png?resizew=164)
(1)在图中作出截面图形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)当点
![](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/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
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