题型:解答题-证明题
难度:0.85
引用次数:120
题号:21551258
如图所示的几何体中,四边形为正方形,
.
![](/uploads/image/idq21133stem/f4a30d0e07484bd7a7a93033f128b70c.png)
(1)求证:![](/uploads/image/squformula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
平面
;
(2)若
,平面
平面.若
为
中点,求证:
.
![](/uploads/image/squformula/6ab1006748f0a9c2181e1144f9a7d9c1.png)
![](/uploads/image/idq21133stem/f4a30d0e07484bd7a7a93033f128b70c.png)
(1)求证:
![](/uploads/image/squformula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](/uploads/image/squformula/fb31ef428bd9de9bc875b343feded3c7.png)
![](/uploads/image/squformula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)若
![](/uploads/image/squformula/a775a5f8a5f08c08c67a1e5eaf8c823c.png)
![](/uploads/image/squformula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](/uploads/image/squformula/a0ed1ec316bc54c37c4286c208f55667.png)
![](/uploads/image/squformula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](/uploads/image/squformula/f392902d611863c6908a48e696e7bd8f.png)
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(已下线)专题04平面与平面的位置关系(2个知识点8种题型)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)
更新时间:2024-01-27 18:24:13
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解答题-证明题
|
较易
(0.85)
名校
解题方法
【推荐1】如图,在四棱锥
中,底面为正方形,
分别是
的中点.
(1)求证:
平面
;
(2)求证:平面
平面
.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/58f9759f5185ecb46de48720ce636860.png)
![](/uploads/image/squformula/fe9588e1e9ca7c10d83ffc723d9d4c32.png)
![](/uploads/image/idqe2119/e97135b1-2a20-4e6f-8760-d75b0cd6bfc0.png)
(1)求证:
![](/uploads/image/squformula/06222ee533c2484ab25321a6abbf98cb.png)
![](/uploads/image/squformula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:平面
![](/uploads/image/squformula/a1fd975b889bfe7ddcec0de56b6f23ee.png)
![](/uploads/image/squformula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近半年使用:0次
2023-10-31更新
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710次组卷
解答题-证明题
|
较易
(0.85)
【推荐2】如图,
是边长为4的正三角形,d,e分别是边ab,ac的中点,以de为折痕把
折起,使点a到达点p的位置,且
,m是pb的中点.
![](/uploads/image/idq21722stem/a5fd834f-391c-48db-a994-d7b6ff9be81a.png)
(1)求证:
平面pec
(2)求三棱锥
的体积.
![](/uploads/image/squformula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](/uploads/image/squformula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](/uploads/image/squformula/9f22f74a1995a5b5fa2a0536606ce1df.png)
![](/uploads/image/idq21722stem/a5fd834f-391c-48db-a994-d7b6ff9be81a.png)
(1)求证:
![](/uploads/image/squformula/6c14a7920527b3b5cc019910af3a3cf5.png)
(2)求三棱锥
![](/uploads/image/squformula/31ed9b5930aff911cbecc862a72d7173.png)
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2021-01-10更新
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解答题-证明题
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较易
(0.85)
名校
【推荐3】如图,在四棱锥
中,底面是边长为1的正方形,
底面
,点
是棱的中点.
![](/uploads/image/idqe215/d5a12034-24c1-4663-aa5f-d238d2a696da.png)
(1)求证:
平面
;
(2)求
与平面所成角.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](/uploads/image/squformula/02af72e5dd2611bd776df97af6f2e2a2.png)
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/idqe215/d5a12034-24c1-4663-aa5f-d238d2a696da.png)
(1)求证:
![](/uploads/image/squformula/30067b7b236d17af8a462f96a58d11bd.png)
![](/uploads/image/squformula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)求
![](/uploads/image/squformula/d2be49c37e30a3ced0364c3e74d8c687.png)
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2018-12-27更新
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612次组卷
解答题-问答题
|
较易
(0.85)
解题方法
【推荐1】如图,在三棱锥
中,
,点p为线段mc上的点.
![](/uploads/image/idqe2128/15a3663d-d413-4333-86ec-849955d43142.png)
(1)若
平面pab,试确定点p的位置,并说明理由;
(2)若
,
,
,求三棱锥
的体积.
![](/uploads/image/squformula/f5d90f940f5693b22ddf2e7c761887d8.png)
![](/uploads/image/squformula/e51fc14e302d27f34c7d8b9531c98a71.png)
![](/uploads/image/idqe2128/15a3663d-d413-4333-86ec-849955d43142.png)
(1)若
![](/uploads/image/squformula/3fb7c585995d694d03475797830ca98f.png)
(2)若
![](/uploads/image/squformula/0b87f92a36e34f4a76360276adeb0914.png)
![](/uploads/image/squformula/ced06b71073e1bb777f326f06016ce17.png)
![](/uploads/image/squformula/c093d0b6f7727e73f36d39c1c8beeef2.png)
![](/uploads/image/squformula/f5d90f940f5693b22ddf2e7c761887d8.png)
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2022-02-13更新
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255次组卷
解答题-证明题
|
较易
(0.85)
名校
解题方法
【推荐2】如图,四棱锥
的底面是矩形,侧面
是正三角形,
,
,
分别为
的中点.
![](/uploads/image/idqe217/c804b2fa-800c-4c4f-997f-ae5c8b242dd5.png)
(1)求证:
;
(2)求平面
与平面
所成角的锐二面角的余弦值.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/1e582d73b96ba649378379c3074d506d.png)
![](/uploads/image/squformula/b38154f661a1c7e0b1e7d03dda8f97d5.png)
![](/uploads/image/squformula/e2ced8225ff27c8e3e1897b8629312d5.png)
![](/uploads/image/squformula/a1da2078b8e4cb44d7147917152d601e.png)
![](/uploads/image/squformula/21d6efca23a04c9c25e8d6c8ccd78e73.png)
![](/uploads/image/idqe217/c804b2fa-800c-4c4f-997f-ae5c8b242dd5.png)
(1)求证:
![](/uploads/image/squformula/141ee0cedfea5ae83aaac1106e2cc259.png)
(2)求平面
![](/uploads/image/squformula/42c12f863669a9c6233fdead272b4d7d.png)
![](/uploads/image/squformula/d1df4b17b68b857bc4a5c34dfd3881a7.png)
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2021-01-12更新
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213次组卷
解答题-证明题
|
较易
(0.85)
解题方法
【推荐3】如图,在四棱锥
中,
底面,且底面为正方形,
,
分别是
的中点.
![](/uploads/image/idqe2222/da842587-c0f9-403a-9158-11b1172c14b6.png)
(1)求证:
;
(2)求证:平面
平面
.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/5a1b49f64e0065edad868b25e9fcada3.png)
![](/uploads/image/squformula/40d4d36ae30487030b827ce9413b9f13.png)
![](/uploads/image/squformula/0b199a99e53d67ff4abf233930961a29.png)
![](/uploads/image/squformula/66313f1b282e75f91c6fb14d4849c0b5.png)
![](/uploads/image/idqe2222/da842587-c0f9-403a-9158-11b1172c14b6.png)
(1)求证:
![](/uploads/image/squformula/fa1ac7e4a2bcadf49838113ab6d95950.png)
(2)求证:平面
![](/uploads/image/squformula/a1fd975b889bfe7ddcec0de56b6f23ee.png)
![](/uploads/image/squformula/852aabd89edffc1b94344ff3f1f31ccd.png)
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【推荐1】已知梯形
如图1所示,其中
,
,
,四边形是边长为1的正方形,沿
将四边形
折起,使得平面
平面,得到如图2所示的几何体.
![](/uploads/image/idqe218/4a8a5ac4-f188-4d08-ace9-e180931afd22.png)
(1)求证:平面
平面
;
(2)求六面体
的体积.
![](/uploads/image/squformula/8edaecff592cf677f45d8c54340a89f2.png)
![](/uploads/image/squformula/10837e4e6808f75a3c8b54a5af4511d0.png)
![](/uploads/image/squformula/38c5c9cc1ed4bce98b7fae77e70b227f.png)
![](/uploads/image/squformula/faffe3765c15f53305516895aa595a9b.png)
![](/uploads/image/squformula/03902478df1a55bc99703210bccab910.png)
![](/uploads/image/squformula/4e35c534ee351308fbbc2dd287147235.png)
![](/uploads/image/squformula/14d61d6896499f312a2d5c06edecae03.png)
![](/uploads/image/idqe218/4a8a5ac4-f188-4d08-ace9-e180931afd22.png)
(1)求证:平面
![](/uploads/image/squformula/b4a46fbde58e12b1edc038ae9e921722.png)
![](/uploads/image/squformula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求六面体
![](/uploads/image/squformula/5d78d008923973b0529d4f7c9f1a2717.png)
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2021-03-13更新
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解答题-证明题
|
较易
(0.85)
解题方法
【推荐2】如图,正方形abcd和平面四边形acef所在的平面互相垂直,
平面,
⊥
,
,
.
(1)求证:
平面
.
(2)求证:平面
平面
.
![](/uploads/image/squformula/06222ee533c2484ab25321a6abbf98cb.png)
![](/uploads/image/squformula/12a477603f3f88c3b48352b6130f9ad5.png)
![](/uploads/image/squformula/60ef95894ceebaf236170e8832dcf7e3.png)
![](/uploads/image/squformula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](/uploads/image/squformula/560439a9b6c535ff5037c950283371cf.png)
![](/uploads/image/idqe2810/d054c236-54d4-4a00-832d-389759cddf99.png)
(1)求证:
![](/uploads/image/squformula/932a04304f2d4975955d4baabb2deeea.png)
![](/uploads/image/squformula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)求证:平面
![](/uploads/image/squformula/b8f5ba965420dfd5aa4da211682df096.png)
![](/uploads/image/squformula/134ef0b1a2669a09f05bd4dc2496f706.png)
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2023-08-09更新
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335次组卷
解答题-问答题
|
较易
(0.85)
解题方法
【推荐3】如图,在三棱锥
中,平面
平面
,
,
,o,m分别为
,
的中点.
![](/uploads/image/idqe2128/1404f8ab-1720-4cf3-be12-292d1b749030.png)
(1)证明:
平面
;
(2)求四棱锥
的体积.
![](/uploads/image/squformula/63397cda22cb1fad59cf966dfb588643.png)
![](/uploads/image/squformula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](/uploads/image/squformula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](/uploads/image/squformula/e4959250cb4f4289b7c5400c7bee0426.png)
![](/uploads/image/squformula/7e2e437445c2743a73be2d96cd1b1f2a.png)
![](/uploads/image/squformula/60ef95894ceebaf236170e8832dcf7e3.png)
![](/uploads/image/squformula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](/uploads/image/idqe2128/1404f8ab-1720-4cf3-be12-292d1b749030.png)
(1)证明:
![](/uploads/image/squformula/f3e126c16032892966489053f44b9048.png)
![](/uploads/image/squformula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求四棱锥
![](/uploads/image/squformula/82fbcab0d22d1a9a29ea4abafac05036.png)
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2021-09-13更新
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