知能综合检测(二十三)

知能综合检测(二十三)

（40分钟 60分）

一、选择题(每小题5分，共20分)

1. (2012·河南中考)如下是一种电子计分牌呈现的数字图形，其中既是轴对称图形又是中心对称图形的是( )

2.如图，在方格纸中的△ABC经过变换得到△DEF，正确的变换是( )

(A)把△ABC向右平移6格

(B)把△ABC向右平移4格，再向上平移1格

(C)把△ABC绕着点A，顺时针旋转90°，再向右平移6格

(D)把△ABC绕着点A，逆时针旋转90°，再向右平移6格

3.一名同学想用正方形和圆设计一个图案，要求整个图案关于正方形的某条对角线对称，那么下列图案中不符合要求的是( )

4.如图，将一朵小花放置在平面直角坐标系中第三象限内的甲位置，先将它绕原点O旋转180°到乙位置，再将它向下平移2个单位长到丙位置，则小花顶点A在丙位置中的对应点A′的坐标为( )

(A)(3，1) (B)(1,3)

(C)(3,-1) (D)(1,1)

二、填空题(每小题5分，共15分)

5.在平面直角坐标系中，已知点A(－4，0)，B(0，2)，现将线段AB 向右平移，使A与坐标原点O重合，则B平移后的坐标是_______.

6.(2012·青岛中考)如图， Rt△ABC中，∠ACB=90°,

∠ABC=30°,AC=1,将△ABC绕点C逆时针旋转至

△A′B′C,使得点A′恰好落在AB上，连结BB′，

则BB′的长度为______.

7.如图，△ABC是等腰直角三角形，BC是斜边，点P是△ABC内一点，△ABP绕点A 逆时针旋转后与△ACP′重合，如果AP＝3，那么PP′的长为______.

三、解答题(共25分)

8.(11分)(2012·济宁中考)如图，在平面直角坐标系中，有一Rt△ABC，且

A(－1，3)，B(－3，－1)，C(－3，3)，已知△A1AC1是由△ABC旋转得到的．

(1)请写出旋转中心的坐标是_____，旋转角是_____度；

(2)以(1)中的旋转中心为中心，分别画出△A1AC1顺时针旋转90°，180°的三角形；

(3)设Rt△ABC两直角边BC＝a，AC＝b,斜边AB＝c，利用变换前后所形成的图案证明勾股定理．

【探究创新】

9.(14分)一副直角三角板叠放如图所示，现将含45°角的三角板ADE 固定不动，把含30°角的三角板ABC绕顶点A顺时针旋转α(α=∠

BAD且0°＜α＜180°)，使两块三角板至少有一组边平行.

(1)如图①，α=_____°时，BC∥DE；

(2)请你分别在图②、图③的指定框内，各画一种符合要求的图形，标出α，并完成各项填空：

图②中α=_____°时，_____∥_____；

图③中α=_____°时，_____∥_____.

答案解析

1.【解析】选C.根据轴对称图形和中心对称图形的定义可知，选项C 中的数字图形既是轴对称图形又是中心对称图形.

2.【解析】选D.由题干图可知把△ABC绕点A逆时针旋转90°后，再经过平移可以得到．

知能综合检测5

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