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【330448】初中数学青岛八下第6章测试卷

时间:2025-02-09 11:18:29 作者: 字数:14202字

单元测试卷

一、选择题

1.下列命题中,正确的是 (   )

A. 对角线互相垂直且相等的四边形是菱形                <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. 对角线互相垂直的平行四边形是菱形
C. 对角线互相平分且相等的四边形是菱形                <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 对角线相等的四边形是菱形

2.如图,在矩形ABCD中,对角线ACBD交于点O,以下说法错误的是(  
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A. ∠ABC=90°                                <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. AC=BD                                <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C. OA=OB                                <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. OA=AB

3.已知下列命题中:①矩形是轴对称图形,且有两条对称轴;②两条对角线相等的四边形是矩形;③有两个角相等的平行四边形是矩形;④两条对角线相等且互相平分的四边形是矩形;其中正确的有(  ).

A. 4个                                       B. 3个                                       C. 2个                                       D. 1

4.用两个边长为a的等边三角形纸片拼成的四边形是(  ).

A. 等腰梯形                                  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. 正方形                                  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C. 矩形                                  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 菱形

5.在△ABC中,点EDF分别在ABBCAC上且DE∥CADF∥BA,下列四个判断中不正确的是(    <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A. 四边形AEDF是平行四边形                                   <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. 如果∠BAC=90°,那么四边形AEDF是矩形
C. 如果AD⊥BC,那么四边形AEDF是菱形               <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 如果AD平分∠BAC,那么四边形AEDF是菱形

6.如图,在□ABCD中,如果EF∥AD GH∥CD EFGH相交与点O 那么图中的平行四边形一共有(    .
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A. 4个                                       B. 5个                                       C. 8个                                       D. 9

7.已知▱ABCD的周长为32,AB=4,BC等于(   )

A. 4                                          <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. 12                                          <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C. 24                                          <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 28

8.已知四边形ABCD是平行四边形,再从①AB=BC,②∠ABC=90°,③AC=BD,④AC⊥BD四个条件中,选两个作为补充条件后,使得四边形ABCD是正方形,现有下列四种选法,其中错误的是(  )

A. 选①②                               B. 选①③                          C. 选②④                              D. 选②③

9.下列条件中,不能判定四边形是平行四边形的是( 

A. 两组对边分别平行                                               <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. 一组对边平行,另一组对边相等
C. 两组对边分别相等                                               <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 一组对边平行且相等

10.如图所示,在平行四边形ABCD中,∠ABE=∠AEBAE∥DFDC是∠ADF的角平分线.下列说法正确的是(  )
①BE=CF ②AE是∠DAB的角平分线 ③∠DAE+∠DCF=120°
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A. ①                                B. ①②                                 C. ①②③                                   <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 都不正确

11.如图,DEF分别为Rt△ABCABACBC的中点,AB=2 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> DCEF的大小关系是(  )
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

A. DCEF                              <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> B. DCEF                              <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C. DC=EF                              <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> D. 无法比较

12.如图,在梯形ABCD中,∠ABC=90ºAE∥CDBCEOAC的中点,AB= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> AD=2BC=3,下列结论:
①∠CAE=30º;②AC=2AB;③S△ADC=2S△ABE;④BO⊥CD,其中正确的是()
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>  

A. ①②③                         B. ②③④                        <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> C. ①③④                            D. ①②③④


二、填空题

13.矩形ABCD的对角线ACBD相交于点O,∠AOD=120°AC+BD=16,则该矩形的面积为________

14.如图,剪两张等宽对边平行的纸条,随意交叉叠放在一起,转动其中的一张,重合的部分构成了一个四边形,这个四边形是________
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

15.如图,▱ABCD的对角线交于点O,且AB=5,△OCD的周长为13,则▱ABCD的两条对角线长度之和为________

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

16.如图,▱ABCD中,∠A=50°AD⊥BD,沿直线DE将△ADE翻折,使点A
在点A′处,AEBDF,则∠DEF=________ 
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

17.已知菱形的两条对角线长为86,那么这个菱形面积是________,菱形的高________

18.2017个边长为2的正方形,按照如图所示方式摆放,O1 O2 O3 O4 O5 …是正方形对角线的交点,那么阴影部分面积之和等于________
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

19.如图所示,在矩形ABCD中,AB=6AD=8PAD上的动点,PE⊥ACPF⊥BDF,则PE+PF的值为________

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

20.四边形ABCD中,如果AB=DC,当AB________ DC时,四边形ABCD是平行四边形;当AD________ BC时,四边形ABCD是平行四边形.

21.如图,△ABC中,AD=BDAE=ECBC=6,则DE=________

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

22.如图,菱形ABCD的边长为5cm,对角线BD的长为6cm,则菱形ABCD的面积为________ cm2
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>


三、解答题

23.已知:如图,EF分别为▱ABCDADBC的中点,分别连接AFBE交于G,连接CEDF交于点H.求证:EFGH互相平分.

 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>






24.如图,已知△ABC的中线BDCE相交于点OMN分别为OBOC的中点. (Ⅰ)求证:MDNE互相平分;
(Ⅱ)若BD⊥ACEM=2  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> OD+CD=7,求△OCB的面积.
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

25.如图,△ABC中,点OAC边上的一个动点,过点O作直线MN∥BC,设MN交∠BCA的外角平分线CF于点F,交∠ACB内角平分线CEE
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1)求证:EO=FO
2)当点O运动到何处时,四边形AECF是矩形?并证明你的结论;
3)若AC边上存在点O,使四边形AECF是正方形,猜想△ABC的形状并证明你的结论







26.如图,在矩形ABCD中,AB=4cmBC=8cm,点P从点D出发向点A运动,运动到点A即停止;同时点Q从点B出发向点C运动,运动到点C即停止.点PQ的速度的速度都是1cm/s,连结PQAQCP,设点PQ运动的时间为ts).

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1)当t为何值时,四边形ABQP是矩形?

2)当t为何值时,四边形AQCP是菱形?

3)分别求出(2)中菱形AQCP的周长和面积.

答案解析

一、选择题

B D C D C D B D B C C D

二、填空题

13. 16  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

14. 菱形

15. 16

16. 65°

17. 24 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

18. 2016

19.  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

20. 平行;=

21. 3

22. 24

三、解答题

23. 证明:∵EAD的中点,FBC的中点, AE=  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ADCF=  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> BC
四边形ABCD是平行四边形,
∴AD∥BC,∴AE∥CFAE=CF
四边形AFCE是平行四边形,
∴AF∥CE
同理可证:BE∥DF
四边形GFHE是平行四边形,
∴EFGH互相平分

24. (Ⅰ)证明:连接EDMN,∵CEBD是△ABC的中线,
∴EDABAC中点,
∴ED∥BCED=  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> BC
∵MN分别为OBOC的中点,
∴MN∥BCMN=  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> BC
∴ED∥MNED=MN
四边形DEMN是平行四边形,
∴MDNE互相平分;
(Ⅱ)解:由(Ⅰ)可得DN=EM=2  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>
∵BD⊥AC
∴∠ODC=90°
∵NOC的中点,
∴OC=2DN=4  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> (直角三角形斜边中线等于斜边的一半)
∵OD2+CD2=OC2=32
OD+CD2=OD2+CD2+2OD×CD=72=49
2OD×CD=49﹣32=17
OD×CD=8.5
∵OB=2OM=2OD
∴S△OCB=  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> OB×CD=OD×CD=8.5
 <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a>

25. 解:(1)∵CE平分∠ACB
∴∠ACE=∠BCE
∵MN∥BC
∴∠OEC=∠ECB
∴∠OEC=∠OCE
∴OE=OC
同理,OC=OF
∴OE=OF
2)当点O运动到AC中点处时,四边形AECF是矩形.
如图AO=COEO=FO
四边形AECF为平行四边形,
∵CE平分∠ACB
∴∠ACE= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ∠ACB
同理,∠ACF= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ∠ACG
∴∠ECF=∠ACE+∠ACF= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> (∠ACB+∠ACG= <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ×180°=90°
四边形AECF是矩形;
3)△ABC是直角三角形
四边形AECF是正方形,
∴AC⊥EN,故∠AOM=90°
∵MN∥BC
∴∠BCA=∠AOM
∴∠BCA=90°
∴△ABC是直角三角形.

26. 1)解:当四边形ABQP是矩形时,BQ=AP,即:t=8﹣t 解得t=4
答:当t=4时,四边形ABQP是矩形
2)解:设t秒后,四边形AQCP是菱形 AQ=CQ,即  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> =8﹣t时,四边形AQCP为菱形.
解得:t=3
答:当t=3时,四边形AQCP是菱形
3)解:当t=3时,CQ=5,则周长为:4CQ=20cm 面积为:4×8﹣2×  <a href="/tags/4/" title="测试" class="c1" target="_blank">测试</a> <a href="/tags/54/" title="试卷" class="c1" target="_blank">试卷</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/1067/" title="青岛" class="c1" target="_blank">青岛</a> <a href="/tags/1078/" title="初中" class="c1" target="_blank">初中</a> ×3×4=20cm2