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【330475】初中数学人教八下期中测试(3)

时间:2025-02-09 11:33:26 作者: 字数:21704字

期中测试(3

一、选择题

1.如果 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 有意义,那么x的取值范围是(  )

Ax1 Bx1 Cx1 Dx1


2.已知正方形的边长为4cm,则其对角线长是(  )

A8cm B16cm C32cm D4 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> cm


3.下列计算正确的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


4.如图所示,在数轴上点A所表示的数为a,则a的值为(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A.﹣1﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B1﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C.﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D.﹣1+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


5.直角三角形中,两直角边分别是125,则斜边上的中线长是(  )

A34 B26 C8.5 D6.5


6.以下各组线段为边长能组成直角三角形的是(  )

A456 B2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 4 C111213 D51213


7.下列各式是最简二次根式的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


8.能判定四边形ABCD为平行四边形的题设是(  )

AABCDAD=BC BAB=CDAD=BC CA=BC=D DAB=ADCB=CD


9.菱形和矩形一定都具有的性质是(  )

A.对角线相等 B.对角线互相垂直C.对角线互相平分且相等 D.对角线互相平分


10.如图字母B所代表的正方形的面积是(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A12 B13 C144 D194


二、填空题

11.已知长方形的宽是3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,它的面积是18 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,则它的长是   


12.计算:( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2016 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2017=  


13.已知菱形两条对角线的长分别为10cm16cm,则这个菱形的面积是   


14.已知直角三角形两边xy的长满足|x2﹣4|+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =0,则第三边长为  


15.如图,矩形ABCD的对角线ACBD相交于点OCEBDDEAC.若AC=4,则四边形CODE的周长是   

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


16.如图,▱ABCD的对角线ACBD相交于点O,点EF分别是线段AOBO的中点,若AC+BD=24厘米,OAB的周长是18厘米,则EF=   厘米.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


三、解答题

17.计算:

(1) <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ÷ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2)3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )(3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )﹣( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2


18.已知:如图,在RtABC中,ACB=90°CD平分ACBDEBCDFAC,垂足分别为EF,求证:四边形CFDE是正方形.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


19.已知:x= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +1y= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣1,求代数式x2+2xy+y2的值.


20.如图,已知在ABC中,CDABDAC=20BC=15DB=9

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(1)DC的长.

(2)AB的长.


21.如图,四边形ABCD是菱形,AC=8BD=6DHABH

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(1)菱形ABCD的周长;

(2)DH的长.


22.在正方形ABCD中,CE=DF,求证:AEBF

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


23.如图,O为矩形ABCD对角线的交点,DEACCEBD

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(1)试判断四边形OCED的形状,并说明理由;

(2)AB=6BC=8,求四边形OCED的面积.


24.如图,已知ABCDEF是两个边长都为10cm的等边三角形,且BDCF都在同一条直线上,连接ADCE

(1)求证:四边形ADEC是平行四边形;

(2)BD=4cmABC沿着BF的方向以每秒1cm的速度运动,设ABC运动的时间为t秒.

当点B匀动到D点时,四边形ADEC的形状是   形;

B运动过程中,四边形ADEC有可能是矩形吗?若可能,求出t的值;若不可能,请说明理由.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>
























答案

1.如果 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 有意义,那么x的取值范围是(  )

Ax1 Bx1 Cx1 Dx1

【考点】二次根式有意义的条件.

【专题】选择题.

【分析】直接利用二次根式有意义的条件分析得出答案.

【解答】解:由题意得:x﹣10

解得:x1

故选B

【点评】此题主要考查了二次根式有意义的条件,正确把握二次根式的定义是解题关键.


2.已知正方形的边长为4cm,则其对角线长是(  )

A8cm B16cm C32cm D4 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> cm

【考点】勾股定理.

【专题】选择题.

【分析】作一个边长为4cm的正方形,连接对角线,构成一个直角三角形如下图所示:由勾股定理得AC2=AB2+BC2,求出AC的值即可.

【解答】解:如图所示:

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

四边形ABCD是边长为4cm的正方形,

RtABC中,由勾股定理得:

AC= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =4 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> cm

所以对角线的长:AC=4 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> cm

故选D

【点评】本题主要考查勾股定理的应用,应先构造一个直角三角形,在直角三角形中斜边的平方等于两直角边的平方和,作图可以使整个题变得简洁明了.


3.下列计算正确的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】二次根式的混合运算.

【专题】选择题.

【分析】根据二次根式的乘法对A进行判断,根据合并同类二次根式对BC进行判断,根据二次根式的除法对D进行判断.

【解答】解:A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,此选项错误;

B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 不是同类二次根式,不能合并,此选项错误;

C3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,此选项错误;

D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ÷ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,此选项正确;

故选D

【点评】本题考查了二次根式的混合运算,熟练掌握二次根式的性质和运算法则是解题的关键.


4.如图所示,在数轴上点A所表示的数为a,则a的值为(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A.﹣1﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B1﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C.﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D.﹣1+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】勾股定理;实数与数轴.

【专题】选择题.

【分析】A在以O为圆心,OB长为半径的圆上,所以在直角BOC中,根据勾股定理求得圆O的半径OA=OB= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,然后由实数与数轴的关系可以求得a的值.

【解答】解:如图,点A在以O为圆心,OB长为半径的圆上.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

在直角BOC中,OC=2BC=1,则根据勾股定理知OB= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

OA=OB= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

a=﹣1﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故选A

【点评】本题考查了勾股定理、实数与数轴.找出OA=OB是解题的关键.


5.直角三角形中,两直角边分别是125,则斜边上的中线长是(  )

A34 B26 C8.5 D6.5

【考点】直角三角形斜边上的中线;勾股定理.

【专题】选择题.

【分析】利用勾股定理列式求出斜边,再根据直角三角形斜边上的中线等于斜边的一半解答.

【解答】解:由勾股定理得,斜边= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =13

所以,斜边上的中线长= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ×13=6.5

故选D

【点评】本题考查了直角三角形斜边上的中线等于斜边的一半的性质,勾股定理,熟记性质是解题的关键.


6.以下各组线段为边长能组成直角三角形的是(  )

A456 B2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 4 C111213 D51213

【考点】勾股定理的逆定理.

【专题】选择题.

【分析】根据勾股定理的逆定理可知,当三角形中三边的关系为:a2+b2=c2时,则三角形为直角三角形.

【解答】解:A42+5262,不符合勾股定理的逆定理,不能组成直角三角形,故选项错误;

B22+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 242,不符合勾股定理的逆定理,不能组成直角三角形,故选项错误;

C112+122132,不符合勾股定理的逆定理,不能组成直角三角形,故选项错误;

D52+122=132,符合勾股定理的逆定理,能组成直角三角形,故选项正确.

故选D

【点评】此题考查的知识点是勾股定理的逆定理,解答此题要用到勾股定理的逆定理:已知三角形ABC的三边满足:a2+b2=c2时,则三角形ABC是直角三角形.解答时,只需看两较小数的平方和是否等于最大数的平方.


7.下列各式是最简二次根式的是(  )

A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】最简二次根式.

【专题】选择题.

【分析】利用最简二次根式定义判断即可.

【解答】解:A <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不符合题意;

B <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 为最简二次根式,符合题意;

C <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不符合题意;

D <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,不符合题意,

故选B

【点评】此题考查了最简二次根式,熟练掌握最简二次根式定义是解本题的关键.


8.能判定四边形ABCD为平行四边形的题设是(  )

AABCDAD=BC BAB=CDAD=BC CA=BC=D DAB=ADCB=CD

【考点】平行四边形的判定.

【专题】选择题.

【分析】根据两组对边分别平行的四边形是平行四边形,两组对边分别相等的四边形是平行四边形;一组对边平行且相等的四边形是平行四边形;两组对边分别相等的四边形是平行四边形;两组对角分别相等的四边形是平行四边形可得答案.

【解答】解:AABCDAD=BC不能判定四边形ABCD为平行四边形,故此选项错误;

BAB=CDAD=BC判定四边形ABCD为平行四边形,故此选项正确;

CA=BC=D不能判定四边形ABCD为平行四边形,故此选项错误;

DAB=ADCB=CD不能判定四边形ABCD为平行四边形,故此选项错误;

故选B

【点评】此题主要考查了平行四边形的判定,关键是掌握平行四边形的判定定理.


9.菱形和矩形一定都具有的性质是(  )

A.对角线相等 B.对角线互相垂直C.对角线互相平分且相等 D.对角线互相平分

【考点】菱形的性质;矩形的性质.

【专题】选择题.

【分析】根据矩形的对角线的性质(对角线互相平分且相等),菱形的对角线性质(对角线互相垂直平分)可解.

【解答】解:菱形的对角线互相垂直且平分,矩形的对角线相等且平分.菱形和矩形一定都具有的性质是对角线互相平分.

故选D

【点评】此题主要考查矩形、菱形的对角线的性质.熟悉菱形和矩形的对角线的性质是解决本题的关键.


10.如图字母B所代表的正方形的面积是(  )

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A12 B13 C144 D194

【考点】勾股定理.

【专题】选择题.

【分析】由图可知在直角三角形中,已知斜边和一直角边,求另一直角边的平方,用勾股定理即可解答.

【解答】解:由题可知,在直角三角形中,斜边的平方=169,一直角边的平方=25

根据勾股定理知,另一直角边平方=169﹣25=144,即字母B所代表的正方形的面积是144

故选C

【点评】此题比较简单,关键是熟知勾股定理:在直角三角形中两条直角边的平方和等于斜边的平方.


11.已知长方形的宽是3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,它的面积是18 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,则它的长是   

【考点】二次根式的除法.

【专题】填空题.

【分析】直接利用二次根式的除法运算法则计算得出答案.

【解答】解:长方形的宽是3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,它的面积是18 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

它的长是:18 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ÷3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =6 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故答案为:6 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】此题主要考查了二次根式的应用,正确掌握二次根式的除法运算法则是解题关键.


12.计算:( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2016 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2017=  

【考点】二次根式的混合运算.

【专题】填空题.

【分析】先根据积的乘方得到原式=[ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ]2016 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ),然后利用平方差公式计算.

【解答】解:原式=[ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ]2016 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=2﹣32016 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

故答案为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的计算:先把各二次根式化为最简二次根式,再进行二次根式的乘除运算,然后合并同类二次根式.


13.已知菱形两条对角线的长分别为10cm16cm,则这个菱形的面积是   

【考点】菱形的面积.

【专题】填空题.

【分析】根据菱形的面积等于对角线乘积的一半列式计算即可得解.

【解答】解:菱形两条对角线的长分别为10cm16cm

菱形的面积S= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ×10×16=80cm2).

故答案为:80cm2

【点评】本题考查了菱形的面积的求法,熟练掌握菱形的面积等于对角线乘积的一半是解题的关键.


14.已知直角三角形两边xy的长满足|x2﹣4|+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =0,则第三边长为  

【考点】解一元二次方程﹣因式分解法;非负数的性质:算术平方根;勾股定理.

【专题】填空题.

【分析】任何数的绝对值,以及算术平方根一定是非负数,已知中两个非负数的和是0,则两个一定同时是0

另外已知直角三角形两边xy的长,具体是两条直角边或是一条直角边一条斜边,应分类讨论.

【解答】解:|x2﹣4|≥0 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

x2﹣4=0y2﹣5y+6=0

x=2或﹣2(舍去),y=23

当两直角边是2时,三角形是直角三角形,则斜边的长为: <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

23均为直角边时,斜边为 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

2为一直角边,3为斜边时,则第三边是直角,长是 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> = <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了有理数加法法则,非负数的性质,另外考查勾股定理的应用.


15.如图,矩形ABCD的对角线ACBD相交于点OCEBDDEAC.若AC=4,则四边形CODE的周长是   

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】菱形的判定与性质;矩形的性质.

【专题】填空题.

【分析】先证明四边形CODE是平行四边形,再根据矩形的性质得出OC=OD,然后证明四边形CODE是菱形,即可求出周长.

【解答】解:CEBDDEAC

四边形CODE是平行四边形,

四边形ABCD是矩形,

OC= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AC=2OD= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> BDAC=BD

OC=OD=2

四边形CODE是菱形,

DE=CEOC=OD=2

四边形CODE的周长=2×4=8

故答案为:8

【点评】本题考查了菱形的判定与性质以及矩形的性质;证明四边形是菱形是解决问题的关键.


16.如图,ABCD的对角线ACBD相交于点O,点EF分别是线段AOBO的中点,若AC+BD=24厘米,OAB的周长是18厘米,则EF=   厘米.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】三角形中位线定理;平行四边形的性质.

【专题】填空题.

【分析】根据AC+BD=24厘米,可得出出OA+OB=12cm,继而求出AB,判断EFOAB的中位线即可得出EF的长度.

【解答】解:四边形ABCD是平行四边形,

OA=OCOB=OD

AC+BD=24厘米,

OA+OB=12cm

∵△OAB的周长是18厘米,

AB=6cm

EF分别是线段AOBO的中点,

EFOAB的中位线,

EF= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AB=3cm

故答案为:3

【点评】本题考查了三角形的中位线定理,解答本题需要用到:平行四边形的对角线互相平分,三角形中位线的判定定理及性质.


17.计算:

(1) <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ÷ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> × <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> + <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2)3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )(3 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> )﹣( <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2

【考点】二次根式的混合运算.

【专题】解答题.

【分析】(1)先进行二次根式的乘除运算,然后化简后合并即可;

(2)利用完全平方公式和平方差公式计算.

【解答】解:(1)原式= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=4﹣ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=4+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(2)原式=18﹣12﹣3﹣2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +2

=6﹣5+2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

=1+2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【点评】本题考查了二次根式的混合运算:先把各二次根式化简为最简二次根式,然后进行二次根式的乘除运算,再合并即可.


18.已知:如图,在RtABC中,ACB=90°CD平分ACBDEBCDFAC,垂足分别为EF,求证:四边形CFDE是正方形.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

【考点】正方形的判定;角平分线的性质;矩形的判定与性质.

【专题】解答题.

【分析】由题意可得,四边形CFDE是矩形,根据角平分线的性质得到DE=DF,根据有一组邻边相等的矩形是正方形,四边形CFDE是正方形.

【解答】证明:∵∠ACB=90°DEBCDFAC

四边形CFDE是矩形.

CD平分ACBDEBCDFAC

DE=DF

四边形CFDE是正方形(有一组邻边相等的矩形是正方形).

【点评】本题是考查正方形的判别方法,判别一个四边形为正方形主要根据正方形的概念,途经有两种:先说明它是矩形,再说明有一组邻边相等;先说明它是菱形,再说明它有一个角为直角.


19.已知:x= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +1y= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣1,求代数式x2+2xy+y2的值.

【考点】二次根式的混合运算.

【专题】解答题.

【分析】首先利用因式分解把x2+2xy+y2化为(x+y2,然后再代入xy的值进行计算即可.

【解答】解:x= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> +1y= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣1

原式=x+y2

= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 1+ <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ﹣12

=2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> 2

=12

【点评】此题主要考查了二次根式的化简计算,关键是正确把x2+2xy+y2进行因式分解.


20.如图,已知在ABC中,CDABDAC=20BC=15DB=9

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

(1)DC的长.

(2)AB的长.

【考点】勾股定理.

【专题】解答题.

【分析】(1)由题意可知三角形CDB是直角三角形,利用已知数据和勾股定理直接可求出DC的长;

(2)(1)的数据和勾股定理求出AD的长,进而求出AB的长.

【解答】解:(1)CDABD,且BC=15BD=9AC=20

∴∠CDA=CDB=90°

RtCDB中,CD2+BD2=CB2

CD2+92=152

CD=12

(2)RtCDA中,CD2+AD2=AC2

122+AD2=202

AD=16

AB=AD+BD=16+9=25

【点评】本题考查了勾股定理,在任何一个直角三角形中,两条直角边长的平方之和一定等于斜边长的平方.如果直角三角形的两条直角边长分别是ab,斜边长为c,那么a2+b2=c2


21.如图,四边形ABCD是菱形,AC=8BD=6DHABH

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(1)菱形ABCD的周长;

(2)DH的长.

【考点】菱形的性质.

【专题】解答题.

【分析】(1)先依据菱形的性质求得AOOB的长,然后依据勾股定理求得AB的长,最后依据菱形ABCD的周长=4AB求解即可;

(2)S菱形ABCD= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AC•BD=AB•DH,可得到DH= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ,最后将ACBDAB的值代入计算即可.

【解答】解:(1)四边形ABCD是菱形,

ACBDOA=OC= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AC=4OB=OD= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> BD=3

RtABO中,由勾股定理可知AB=5

菱形ABCD的周长=5×4=20

(2)S菱形ABCD= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AC•BD=AB•DH

DH= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =4.8

【点评】本题主要考查的是菱形的性质,掌握菱形的面积公式是解题的关键.


22.在正方形ABCD中,CE=DF,求证:AEBF

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【考点】正方形的性质;全等三角形的判定与性质.

【专题】解答题.

【分析】根据正方形性质得出ABE=C=90°AB=BCBC=CD,求出BE=CF,根据SAS推出ABE≌△BCF,根据全等三角形的性质得出BAE=CBF,求出CBF+∠AEB=90°,即可得出答案.

【解答】证明:四边形ABCD是正方形,

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∴∠ABE=C=90°AB=BCBC=CD

CE=DF

BE=CF

ABEBCF

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∴△ABE≌△BCFSAS),

∴∠BAE=CBF

∵∠ABE=90°

∴∠BAE+∠AEB=90°

∴∠CBF+∠AEB=90°

∴∠BOE=180°﹣90°=90°

AEBF

【点评】本题考查了正方形的性质,全等三角形的性质和判定,能求出ABE≌△BCF是解此题的关键,注意:正方形的四条边都相等,正方形的四个角都是直角.


23.如图,O为矩形ABCD对角线的交点,DEACCEBD

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(1)试判断四边形OCED的形状,并说明理由;

(2)AB=6BC=8,求四边形OCED的面积.

【考点】菱形的判定;平行四边形的判定;矩形的性质.

【专题】解答题.

【分析】(1)首先可根据DEACCEBD判定四边形ODEC是平行四边形,然后根据矩形的性质:矩形的对角线相等且互相平分,可得OC=OD,由此可判定四边形OCED是菱形.

(2)连接OE,通过证四边形BOEC是平行四边形,得OE=BC;根据菱形的面积是对角线乘积的一半,可求得四边形ODEC的面积.

【解答】解:(1)四边形OCED是菱形.

DEACCEBD

四边形OCED是平行四边形,

又在矩形ABCD中,OC=OD

四边形OCED是菱形.

(2)连接OE

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由菱形OCED得:CDOE

BCCD

OEBC(在同一平面内,垂直于同一条直线的两直线平行),

CEBD

四边形BCEO是平行四边形;

OE=BC=87分)

S四边形OCED= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> OE•CD= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ×8×6=24

【点评】本题主要考查矩形的性质,平行四边形、菱形的判定,菱形面积的求法;

菱形的判别方法是说明一个四边形为菱形的理论依据,常用三种方法:

定义;

四边相等;

对角线互相垂直平分.


24.如图,已知ABCDEF是两个边长都为10cm的等边三角形,且BDCF都在同一条直线上,连接ADCE

(1)求证:四边形ADEC是平行四边形;

(2)BD=4cmABC沿着BF的方向以每秒1cm的速度运动,设ABC运动的时间为t秒.

当点B匀动到D点时,四边形ADEC的形状是   形;

B运动过程中,四边形ADEC有可能是矩形吗?若可能,求出t的值;若不可能,请说明理由.

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【考点】平行四边形的判定与性质;等边三角形的性质;矩形的判定.

【专题】解答题.

【分析】(1)因为ABCDEF是两个边长为10cm的等边三角形所以AC=DF,又ACD=FDE=60°,可得ACDE,所以四边形ADEC是平行四边形;

(2)根据有一组邻边相等的四边形是菱形即可得到结论;

根据有一个角是直角的平行四边形是矩形即可得到结论.

【解答】(1)证明:∵△ABCDEF是两个边长为10cm的等边三角形.

AC=DEACD=FDE=60°

ACDE

四边形ADEC是平行四边形.

(2)解:t=4秒时,ADEC是菱形,

此时BD重合,AD=DE

∴▱ADEC是菱形,

若平行四边形ADEC是矩形,则ADE=90°

∴∠ADC=90°﹣60°=30°

同理DAB=30°=ADC

BA=BD

同理FC=EF

FB重合,

t=10+4÷1=14秒,

t=14秒时,四边形ADEC是矩形.

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【点评】本题考查了平行四边形、菱形和矩形的判定,勾股定理,熟记这些定理是解题的关键.