旋转的有关概念及性质(2).doc

班级_____________________ 姓名____________________ 考场号____________ 考号___________

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一、选择题
1. (2014 贵州省遵义市)
如图，已知△ABC中，∠C=90°，AC=BC=，将△ABC绕点A顺时针方向旋转60°到△AB′C′的位置，连接C′B，则C′B的长为（　　）

A．
2﹣
B．

C．
﹣1
D．
1

填空题）

2. (2014 黑龙江省哈尔滨市) （2014黑龙江哈尔滨市，9，3分）如图，在Rt△ABC中，∠ACB＝90°，∠B＝60°，BC＝2，△A/B/C是由△ABC绕C点顺时针旋转得到，其中点A/与点A是对应点，点B/与点B是对应点，连接AB/，且A、B/、A/在同一条直线上，则AA/的长为（ ）
（A）6 （B） （C） （D）3
第9题图

3. (2014 湖北省随州市)
在等边△ABC中，D是边AC上一点，连接BD，将△BCD绕点B逆时针旋转60°，得到△BAE，连接ED，若BC=5，BD=4．则下列结论错误的是（　　）

A．
AE∥BC
B．
∠ADE=∠BDC

C．
△BDE是等边三角形
D．
△ADE的周长是9

4. (2014 湖南省长沙市) 下列四个圆形图案中，分别以它们所在圆的圆心为旋转中心，顺时针旋转120°后能与原图形完全重合的是( )

5. (2014 山东省莱芜市) 如图，AB为半圆的直径，且AB＝4,半圆绕点B顺时针旋转45°，点A旋转到A′的位置，则图中阴影部分的面积为（ ）
( 第8题图)

A. B. 2 C. D. 4

6. (2014 山东省泰安市) 将两个斜边长相等的三角形纸片如图（1）放置，其中∠ACH=∠CED=90°，∠A=45°，
∠D=30°，把△DCE绕点C顺时针旋转15°得到△D`CE`。如图（2），连接DB，则∠E`D`B的度数为（ ）
（A）10° （B）20° （C）7.5° （D）15°

7. (2014 浙江省金华市) 如图，将Rt△ABC绕直角顶点C顺时针旋转90°，得到△A′B′C，
连结AA′，若∠1=20°，则∠B的度数是（ ▲ )
A.70° B.65° C.60° D.55°
A
B
C
A′
B′
1
第8题图

8. (2014 四川省资阳市) 如图，在Rt△ABC中，∠BAC=90°，如果将该三角形绕点A按顺时针方向旋转到△AB1C1的位置，点B1恰好落在边BC的中点处，那么旋转的角度等于（ ）
A．55° B．60° C．65° D．80°

9. (2014 四川省遂宁市) 如图，在Rt△ABC中，∠ACB=90°，∠ABC=30°，将△ABC绕点C顺时针旋转至△A′B′C，使得点A′恰好落在AB上，则旋转角度为（　　）

A．
30°
B．
60°
C．
90°
D．
150°

10. (2014 浙江省义乌市) 如图，将Rt△ABC绕直角顶点C顺时针旋转90°，得到△A′B′C，
连结若∠1=20°，则∠B的度数是（ ▲ )
A.70° B.65° C.60° D.55°
A
B
C
A′
B′
1
第8题图

11. (2014 广西桂林市) 如图，在△ABC中，∠CAB=70°，将△ABC绕点A逆时针旋转到△AB`C`的位置，使得CC`∥AB，则∠BAB`的度数是（ ）
A．70° B．35° C．40° D．50°

二、填空题
12. (2014 黑龙江省牡丹江市) 如图，在△ABC中，AC=BC=8，∠C=90°，点D为BC的中点，将△ABC绕点D逆时针旋转45°，得到△A’B’C’，B’C’与AB交于点E，则= .

13. (2014 湖南省邵阳市) 如图（九），在平面直角坐标系xOy中，已知点A（3，4），将OA绕坐标原点O逆时针旋转90°到OA′，则点A′的坐标是 .

14. (2014 湖南省益阳市) 如图4，将等边绕顶点顺时针方向旋转，使边与重合得，的中点的对应点为，则的度数是 ．
图4
B
C
A
F
E
D

15. (2014 山东省济宁市) 如图（1），有两个全等的正三角形ABC和ODE，点O、C分别为△ABC、△DEO的重心；固定点O，将△ODE顺时针旋转，使得OD 经过点C，如图（2）所示，则图（2）中四边形OGCF与△OCH面积的比为 .

16. (2014 江西省) 如图，是将菱形ABCD以点O为中心按顺时针方向分别旋转90°，180°，270°后形成的图形．若∠BAD＝60°，AB＝2，则图中阴影部分的面积为______．

(第13题)
O
A
B
C
D

17. (2014 江西省抚州市) 如图，两块完全相同的含30°角的直角三角板ABC和重合在一起，将三角板绕其顶点按逆时针方向旋转角α（0°< α≤90°），有以下四个结论：
①当α=30°时，与的交点恰好为的中点；②当α=60°时，恰好经过点；
③在旋转过程中，存在某一时刻，使得； ④在旋转过程中，始终存在，其中结论正确的序号是 .(多填或填错得0分，少填酌情给分）

18. (2014 广东省中山市) 如图，△ABC绕点A顺时针旋转45°得到△A′B′C′，若∠BAC=90°，AB=AC=，则图中阴影部分的面积等于　_________　．

三、画(作)图题
19. (2014 黑龙江省龙东地区) 如图，方格纸中每个小正方形的边长都是1个单位长度，Rt△ABC的三个顶点A（－2，2），B（0，5），C（0，2）。
（1） 将△ABC以点C为旋转中心旋转180°，得到△A1B1C， 请画出△A1B1C的图形 。
（2）平移△ABC，使点A 的对应点A2坐标为（－2，－6），请画出平移后对应的△A2B2C2的图形。
（3）若将△A1B1C绕某一点旋转可得到△A2B2C2，请直接写出旋转中心的坐标。
A
B
C
O
x
y

四、应用题
20. (2014 湖北省咸宁市) _ich
_
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