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【323838】2024八年级数学上学期期末综合素质评价(新版)冀教版

时间:2025-01-15 20:48:34 作者: 字数:9918字
简介:


期末综合素质评价

 

 

 





一、选择题(每题3分,共36)

1[2022·淄博]下列图案中,既是轴对称图形又是中心对称图形的是(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

A B C D

2下列计算正确的是(  )

A. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> B. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> × <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 6

C. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> D. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ÷ <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 4

3[母题教材P3练习T1] 要使分式 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 有意义,则x的取值范围是(  )

A. x1 B. x1 C. x≠1 D. x1

4[2023·盐城]小华将一副三角板(∠C=∠D90°,∠B30°,∠E45°)按如图所示的方式摆放,其中ABEF,则∠1的度数为(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(4)

A.45° B.60° C.75° D.105°

5ab均为正整数,且a <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> b <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,则ab的最小值是(  )

A.3 B.4 C.5 D.6

6[母题教材P20练习T1] 分式方程 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 的解是(  )

A. x2 B. x1 C. x <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> D. x=-2

7[2022·荆门]数学兴趣小组为测量学校A与河对岸的科技馆B之间的距离,在A的同岸选取点C,测得AC30,∠A45°,∠C90°,如图,据此可求得AB之间的距离为(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(7)

A.20 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> B.60 C.30 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> D.30

8下列命题:①两个周长相等的三角形是全等三角形;②两个周长相等的直角三角形是全等三角形;③两个周长相等的等腰三角形是全等三角形;④两个周长相等的等边三角形是全等三角形.其中,真命题有(  )

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

9如图,△ABC的三边ABBCCA的长分别是203040,三条角平分线将△ABC分为三个小三角形,则SABOSBCOSCAO等于(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(9)

A.1∶1∶1 B.1∶2∶3 C.2∶3∶4 D.3∶4∶5

10如图,△ABC和△DCE都是边长为4的等边三角形,点BCE在同一条直线上,连接BD,则BD的长度为(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(10)

A. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> B.2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> C.3 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> D.4 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

11[新考法等积法] 如图,在△ABC中,ABAC13BC10,点DBC的中点,DEAB,垂足为点E,则DE等于(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(11)

A. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> B. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> C. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> D. <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

12如图,在△ABC中,ADBC,垂足为DEF垂直平分AC,交AC于点F,交BC于点E,连接AE,已知BDDE,若

ABC的周长为26cmAF5cm,则DC的长为(  )

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(12)

A.7cm B.8cm C.9cm D.10cm

二、填空题(每题3分,共12)

13[母题教材P99做一做] 计算 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 10 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 的结果为    .

14[母题教材P34练习T1] 命题“全等三角形的对应边相等”的逆命题是    

逆命题是    (填“真命题”或“假命题”).

15如图,点ABC分别在边长为1的正方形网格图顶点处,则∠ABC    .

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(15)

16如图,在四边形ABCD中,AB3AD4,∠DAB30°,且BCCDDB,则AC的长为    .

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

(16)

三、解答题(1722题每题10分,第2312分,共72)

17[2024·邯郸永年区期末]已知a <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> b <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

(1)ab的值;

(2)a23abb2





18[母题教材P16做一做] 先化简,再求值: <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ÷ <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,其中x <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .





19[母题教材P160练习T2] 如图,BDCE分别是△ABC的高,且BECD.求证:Rt△BEC≌Rt△CDB.

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>








20如图,在四边形ABCD中,ADBCECD的中点,连接AEBEBEAE,分别延长AEBC交于点F.求证:

(1)ADFC

(2)ABBCAD.

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>







21如图,AD平分∠BACADBD,垂足为DDEAC.求证:△BDE是等腰三角形.

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>






22[2024·石家庄第八十九中学期末]为了加快推进环境建设,构建生态宜居城市,实现“河畅、水清、岸绿、景美”的目标,九龙坡区计划安排甲、乙两个施工队对一条全长为4100米的河道进行清淤施工.经调查知:甲队每天清淤的河道长度是乙队每天清淤的河道长度的1.5倍,甲队清淤1200米的河道比乙队清淤同样长的河道少用2.

(1)甲、乙两队每天清淤的河道长度分别是多少米?

(2)若该条河道先由甲队单独清淤2天,余下的河道由甲、乙两队合

作清淤.已知甲队施工一天的费用为3.2万元,乙队施工一天的费用为2.8万元,求完成该条河道清淤施工的总费用.






23课外兴趣小组活动时,老师出示了如下问题:如图①,已知在四边形ABCD中,AC平分∠DAB,∠DAB60°,∠B与∠D互补.求证:ABAD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.

小敏反复探索,不得其解.她想,可先将四边形ABCD特殊化,再进一步解决该问题.

(1)由特殊情况入手,添加条件:“∠B=∠D”.如图②,请你证明

ABAD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.

(2)受到(1)的启发,在原问题中,添加辅助线:过C点分别作AB

AD的垂线,垂足分别为点EF,如图③.请你证明ABAD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>


答案

一、1. D 2. C 3. C 4. C

5. B【点拨】∵ <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,∴2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 3,∵a <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,且a为正整数,∴a的最小值为3,∵ <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,∴1 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 2,∵b <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ,且b为正整数,∴b的值为1,∴ab的最小值为314.

6. A 7. C

8. A【点拨】两个周长相等的三角形不一定全等,故①是假命题;两个周长相等的直角三角形不一定全等,故②是假命题;两个周长相等的等腰三角形不一定全等,故③是假命题;两个周长相等的等边三角形一定全等,因为三条边对应相等,故④是真命题.故真命题有1.

9. C

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

【点拨】如图,过点O分别作ABBCCA的垂线,垂足分别为点FDE

由角平分线的性质得ODOEOF

∵△ABC的三边ABBCCA的长分别是203040

SABO∶SBCO∶SCAO=( <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AB·OF <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> BC·OD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> CA·OE)=AB∶BC∶CA203040234.

10. D【点拨】∵△ABC和△DCE都是边长为4的等边三角形,∴BCCDDECE4,∠DCE=∠CDE60°,∴BE8,∠BCD120°

∴∠CBD=∠CDB30°,∴∠BDE90°

BD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 4 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

11. C【点拨】连接AD,则由已知易得ADBCBD5,在Rt△ABD中,根据勾股定理,得AD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 12.根据三角形面积公式,可得 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AB·DE <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> BD·AD,即13DE5×12,解得DE <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

12. B【点拨】∵△ABC的周长为26cm

ABBCAC26cm.

EF垂直平分ACAF5cm

AC2AF10cmEAEC,∴ABBC16cm.

ADBCBDDE,∴ABAE,∴ABEC

ABBDECDE <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> ABBC)=8cm

DCDECE8cm.

二、13.4 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

14.三边对应相等的三角形全等;真命题

15.45°【点拨】如图,连接AC

根据题意,可知BC212225AC212225AB2123210.

AB2AC2BC2ACBC

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

∴△ABC为等腰直角三角形,

∴∠ABC45°.

16.5【点拨】以AC为边向上作等边三角形AEC,连接DE,如图,

 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

在等边三角形AEC中,

ACAEEC,∠EAC=∠AEC=∠ECA60°.

BCCDDB

∴△BDC是等边三角形,

∴∠DBC=∠BDC=∠DCB60°,∴∠ECA=∠ECD+∠DCA60°=∠DCB=∠BCA+∠DCA

∴∠ECD=∠BCA.

BCCDECAC

∴△ABC≌△EDCSAS),

∴∠BAC=∠DECABDE.

∵∠DAB30°,∴∠DAC+∠BAC30°

∴∠DAC+∠DEC30°.

∵∠EAC+∠AEC60°60°120°

∴∠DEA+∠DAE=(∠EAC+∠AEC)-(∠DAC+∠DEC)=90°

∴∠EDA90°

AB3,∴DEAB3.

又∵AD4

Rt△EDA中,AE <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 5

ACAE5.

三、17.【解】(1a <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

b <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

ab <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

2)∵ab=( <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> × <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> )=1

a23abb2=(ab25ab=(2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 25×11257.

18.【解】原式= <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> · <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> · <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

x <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 时,原式= <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> .

19.【证明】∵BDCE分别是△ABC的高,

∴∠BEC=∠CDB90°.

Rt△BECRt△CDB中, <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>

Rt△BEC≌Rt△CDBHL.

20.【证明】(1)∵ADBC,∴∠D=∠ECF.

ECD的中点,∴DECE.

又∵∠AED=∠FEC

∴△ADE≌△FCEASA.∴ADFC.

2)由(1)知△ADE≌△FCE,∴AEFE.

又∵BEAF,∴ABFB.

CFAD,∴ABFBBCCFBCAD.

21.【证明】∵DEAC,∴∠CAD=∠ADE.

AD平分∠BAC,∴∠CAD=∠DAE.

∴∠DAE=∠ADE.

ADBD

∴∠DAE+∠B90°,∠ADE+∠BDE90°

∴∠B=∠BDE.

BEDE,即△BDE是等腰三角形.

22.【解】(1)设乙队每天清淤的河道长度是x米,则甲队每天清淤的河道长度是1.5x米,

根据题意,得 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a>  <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> 2,解得x200

经检验,x200是所列方程的解,且符合题意,

1.5x1.5×200300

答:甲队每天清淤的河道长度是300米,乙队每天清淤的河道长度是200米;

2)设乙队施工y天,则甲队施工(y2)天,

根据题意,得300y2)+200y4100,解得y7

3.2y2)+2.8y3.2×72)+2.8×748.4

答:完成该条河道清淤施工的总费用是48.4万元.

23.【证明】(1)∵∠B与∠D互补,且∠B=∠D

∴∠B=∠D90°.

AC平分∠DAB,∠DAB60°

CDCB,∠CAB=∠CAD30°.

CDCBx,则AC2x.

由勾股定理,得AD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> CD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> xAB <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> CB <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> x.

ADAB <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> x <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> x2 <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> x <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC

ABAD <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.

2)由(1)知,AEAF <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.

AC平分∠DABCFADCEAB

CFCE,∠CFD=∠CEB90°.

∵∠ABC与∠D互补,∠ABC与∠CBE互补,

∴∠D=∠CBE,∴△CDF≌△CBE.∴DFBE

ABADAB+(AFFD)=(ABBE)+AFAEAF <a href="/tags/49/" title="上学" class="c1" target="_blank">上学</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/208/" title="学期" class="c1" target="_blank">学期</a> <a href="/tags/279/" title="综合" class="c1" target="_blank">综合</a> <a href="/tags/300/" title="素质" class="c1" target="_blank">素质</a> <a href="/tags/499/" title="评价" class="c1" target="_blank">评价</a> AC.