2017高三·全国·专题练习
1 . (2017广东广州)如图,平面直角坐标系中
是原点,
的顶点
的坐标分别是
,点
把线段
三等分,延长
分别交
于点
,连接
,则下列结论:
①
是
的中点;②
与
相似;③四边形
的面积是
;④
;其中正确的结论是 __________ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e698404fde91350c873592032ea5326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec32dae2a8966c629cdaea0cca4d25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55f18975e22970b8fde117a588d9b681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c87b8e05d61ddc69dbc02772d719d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf33d73483c93f24cc6a1d76ef22ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3c024b213dbe2016bf593071d7856c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f18f78116d37176a4e7a7b5d0764268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82901484b0b4b192cdd45a88c6163aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d754c4ad51e4482e12a615d20a13fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0f572db5c9ca057212b60d9c2163e7.png)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435225088/STEM/e322abc96d32435cbe9db4eb83878547.png?resizew=153)
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2017高三·全国·专题练习
2 . 如图,在矩形ABCD中,E是AD边的中点,BE⊥AC,垂足为F,连结DF,下列四个结论:①△AEF∽△CAB;②tan∠CAD=
;③DF=DC;④CF=2AF,正确的是( )
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435200512/STEM/9f0b7b33ecb64d6595bf4b710fde9769.png?resizew=171)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435200512/STEM/9f0b7b33ecb64d6595bf4b710fde9769.png?resizew=171)
A.①②③ | B.②③④ | C.①③④ | D.①②④ |
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2017高三·全国·专题练习
3 . (2017湖北随州)如图,在矩形ABCD中,AB<BC,E为CD边的中点,将△ADE绕点E顺时针旋转180°,点D的对应点为C,点A的对应点为F,过点E作ME⊥AF交BC于点M,连接AM、BD交于点N,现有下列结论:
①AM=AD+MC;②AM=DE+BM;③DE2=AD•CM;④点N为△ABM的外心.其中正确的个数为( )
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435159552/STEM/3362b1a3c73247d8ac78171f49a94aa8.png?resizew=243)
①AM=AD+MC;②AM=DE+BM;③DE2=AD•CM;④点N为△ABM的外心.其中正确的个数为( )
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435159552/STEM/3362b1a3c73247d8ac78171f49a94aa8.png?resizew=243)
A.1个 | B.2个 | C.3个 | D.4个 |
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2017高三·全国·专题练习
4 . 如图,点P是正方形ABCD的对角线BD上一点,PE⊥BC于点E,PF⊥CD于点F,连接EF.给出下列五个结论:①AP=EF;②AP⊥EF;③△APD一定是等腰三角形;④∠PFE=∠BAP;⑤PD=
EC.其中正确结论的序号是____________ .
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435380736/STEM/fc9aeb869ee04ea4b28ba7ede19fe259.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435380736/STEM/ea9fe734dae641a7822c22a0a7cf807a.png?resizew=110)
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2017高三·全国·专题练习
5 . 如图,在一张矩形纸片ABCD中,AB=4,BC=8,点E,F分别在AD,BC上,将纸片ABCD沿直线EF折叠,点C落在AD上的一点H处,点D落在点G处,有以下四个结论:
①四边形CFHE是菱形;②线段BF的取值范围为3≤BF≤4;
③EC平分∠DCH;④当点H与点A重合时,EF=
.
以上结论中,你认为正确的有______ .(填序号)
①四边形CFHE是菱形;②线段BF的取值范围为3≤BF≤4;
③EC平分∠DCH;④当点H与点A重合时,EF=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
以上结论中,你认为正确的有
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357956227072/1929155435438080/STEM/790688633b8c49b4b961e564d2a03b16.png?resizew=184)
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2017高三·全国·专题练习
6 . 如图,菱形ABCD的边长为2,∠A=60°,一个以点B为顶点的60°角绕点B旋转,这个角的两边分别与线段AD的延长线及CD的延长线交于点P、Q,设DP=x,DQ=y,则能大致反映y与x的函数关系的图象是( )
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357673521152/1929139633266688/STEM/64e9f8a7f959488da92dbb54bf0caf5c.png?resizew=235)
![](https://img.xkw.com/dksih/QBM/2018/4/16/1925357673521152/1929139633266688/STEM/64e9f8a7f959488da92dbb54bf0caf5c.png?resizew=235)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 选修 4-1:几何证明选讲
已知点
在圆
直径
的延长线上,
切圆
于
点,
分别交
,
于点
,
,
.
![](https://img.xkw.com/dksih/QBM/2017/11/28/1827047244275712/1828939645018112/STEM/53a59f6801fe4ac4bb86594e47f541b4.png?resizew=171)
(1)求证:
为
的平分线;
(2)若
,求
的值.
已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd546aa376d38da2cfbae4a38dcbd01.png)
![](https://img.xkw.com/dksih/QBM/2017/11/28/1827047244275712/1828939645018112/STEM/53a59f6801fe4ac4bb86594e47f541b4.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78dc4f4584665f0db3d9363784c1683.png)
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8 . 如图,已知⊙O的直径AB与弦AC的夹角为35°,过C点的切线PC与AB的延长线交于点P,那么∠P等于( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848850362368/1816566449266688/STEM/304ffc3c6e624c8fa4f26438214df6eb.png?resizew=107)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848850362368/1816566449266688/STEM/304ffc3c6e624c8fa4f26438214df6eb.png?resizew=107)
A.15° | B.20° |
C.25° | D.30° |
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9 . 如图,PA是⊙O的切线,A为切点,PC是⊙O的割线,且PB=
BC,则
等于( )
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848850362368/1816566449258496/STEM/7c9a74053fb14ddbbf745b63add9ce9a.png?resizew=111)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccc2f02416db8211128e18af2d13ecf.png)
![](https://img.xkw.com/dksih/QBM/2017/8/14/1758848850362368/1816566449258496/STEM/7c9a74053fb14ddbbf745b63add9ce9a.png?resizew=111)
A.2 | B.![]() | C.![]() | D.1 |
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10 . 对于半径为4的圆在平面上的投影的说法错误的是( )
A.射影为线段时,线段的长为8 |
B.射影为椭圆时,椭圆的短轴可能为8 |
C.射影为椭圆时,椭圆的长轴可能为8 |
D.射影为圆时,圆的直径可能为4 |
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