题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072440-22609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072440-87596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072440-80488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072440-22609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-97934.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-95129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31253.png)
(2)求二面角A-BF-C的平面角的余弦值;
(3)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-63902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-22093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-37147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-67287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-57530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-26369.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-50073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-56382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-50015.png)
∠
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-70869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-41062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-61396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-70558.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-50317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-32171.png)
∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-87425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-50073.png)
平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-87425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-50073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-91010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-99886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-50073.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-87425.png)
(2)取
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-19158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-41628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-95023.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-90173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-54238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-82620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-19158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-70661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-75491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-19158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072444-14100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-70621.jpg)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-80689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-97768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-89387.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-47977.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-55299.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-15757.jpg)
(3)由(2)知,①当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-88050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-11681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-55773.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-88050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-58920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-42743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-17169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-37147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-29478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-80689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-32171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-80689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-80689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-70869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-29478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-70869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-83061.jpg)
∴ ∠
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-70869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-41062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072442-57530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-24090.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072446-88050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-51649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072448-70487.png)
延长
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072448-15101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-80689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072448-51536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-29478.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072448-51536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-37147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31384.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072448-79645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-37147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31384.png)
∴ 平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-37147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072441-31384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072447-29478.png)
过C作CH⊥NB交NB于H ,连结AH,
由(I)知,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072449-46729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-32171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072443-16921.png)
∴ AC⊥NB, 又∵ CH⊥NB,AC∩CH=C,∴ NB⊥平面ACH ∴AH⊥NB ∴ ∠AHC=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68596.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072449-46559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072449-69819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072449-90968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072449-29180.png)
∵ ∠ACH=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072450-40480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072450-66459.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072450-33280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072445-68003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072450-99077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072451-37081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072451-91283.png)
解析
核心考点
试题【((本小题12分)如图,在梯形中,,,四边形为矩形,平面平面,.(1)求证:平面;(2)求二面角A-BF-C的平面角的余弦值;(3)若点在线段上运动,设平面与平】;主要考察你对线线角等知识点的理解。[详细]
举一反三
A.一个或两个 B.一个或三个 C.一个或四个 D.两个或三个
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072424-14485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072424-61829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072424-15617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072425-81319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072424-61829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072425-82324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072425-85615.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072416-53985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-29721.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-34740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-37495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-61087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-41728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072417-94840.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072418-67134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072418-49862.png)
⑤若
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072418-67101.png)
其中正确命题的序号是_______________(把所有正确命题的序号都填上).
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072410-11608.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072410-47985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072410-49232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072410-10939.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072411-54809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072411-57050.png)
(Ⅱ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072411-39265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072411-64749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072412-28058.jpg)
如图,正方形ABCD、ABEF的边长都是1,而且平面ABCD、ABEF互相垂直,点M在AC上移动,点N在BF上移动,
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072404-25473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072405-62557.png)
(1)求MN的长;
(2)当a为何值时,MN的长最小;
(3)当MN的长最小时,求面MNA与面MNB所成的二面角的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022072405-14135.png)
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