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【324797】2024七年级数学上学期期中综合素质评价 鲁教版五四制

时间:2025-01-15 19:57:35 作者: 字数:12052字
简介:


期中综合素质评价

一、选择题(每题3分,共36)

1[新考向传统文化][2023·湘潭]中国的汉字既象形又表意,不但其形美观,而且寓意深刻.观察下列汉字,其中是轴对称图形的是(  )

A.爱 B.我 C.中 D.华

2.如图,在△ABC中,AB边上的高是(  )

 <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>

(2)

ACD BCE CBF DBG

3[2023·金华]在下列长度的四条线段中,能与长6cm8cm的两条线段围成一个三角形的是(  )

A1cm B2cmC13cm D14cm

4.如果一个三角形三个内角的度数比是2∶3∶4,则它是(  )

A.锐角三角形B.钝角三角形

C.直角三角形D.钝角或直角三角形

5 <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> 将一张正方形纸片按下列方式对折三次,然后沿虚线裁剪,将裁剪后的纸片完全展开,所看到的图案是(  )

 <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 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 B C D

6[新考向知识情境化][2023·日照东港区月考]如图,小敏做了一个角平分仪ABCD,其中ABADBCDC,使仪器上的点APRQ的顶点R重合,调整ABAD,使它们分别落在PRQ的两边上,过点AC画一条射线AEAE就是PRQ的平分线.此角平分仪的画图原理是(  )

 <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>

(6)

ASSS BSAS CASA DAAS

7.如图,在等边三角形ABC中,ADBC边上的高,BDECDF60°,点EF分别在ABAC上,图中与BD相等的线段有(  )

 <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)

A5B6

C7D8

8[情景题生活应用]如图,小明家仿古家具的一块三角形形状的玻璃坏了,需要重新配一块.小明通过打电话给玻璃店老板提供相关数据,为了方便表述,将该三角形记为△ABC,提供下列各组元素的数据,配出来的玻璃不一定符合要求的是(  )

 <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>

(8)

AABBCCA BABBCB

CABACB DABBC

9.已知△ABC的三边分别为abc,满足c2a2b2c22b20,则这个三角形有一个角的度数为(  )

A135°B75°

C45°D30°

10.如图,一棵大树在离地面6m10m两处折成三段,中间一段AB恰好与地面平行,大树顶部落在离大树底部12m远处,则大树折断前的高度是(  )

 <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>

(10)

A14m B16m

C18m D20m

11[2023·威海期末]如图所示的三角形纸片ABC中,BC,将纸片沿过点B的直线折叠,使点C落到AB边上的点E处,折痕为BD.再将纸片沿过点E的直线折叠,点A恰好与点D重合,折痕为EF,若AE2,△ABC的周长为13,则AF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>

(11)

A12 B15 C14 D1

12[新视角规律探究题]如图所示,图中所有的四边形都是正方形,所有的三角形都是等腰直角三角形,且最大的正方形的边长为4.若按照图至图的规律设计图案,则在第n个图中所有等腰直角三角形的面积的和为(  )

 <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)

A4n B8n C4n D32

二、填空题(每题3分,共18)

13.如图所示,人字梯中间一般会设计一个“拉杆”,这样做的依据是    

 <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>

(13)

14.如图,点ABCD在同一条直线上,△ACE≌△DBF,若AD6BC2,则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>

(14)

15.在Rt△ABC中,C90°AB12cmBD平分ABC,交AC于点D,若CD4cm,则 <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>     cm2

16[新趋势跨学科]如图,我们知道,光线射向一个平面镜被反射后,两条光线与平面镜的夹角相等(12).如图,光线照射到平面镜甲上,会反射到平面镜乙上,然后光线又会反射到平面镜甲上,….若α55°γ75°,则β    °

 <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)

17[2023·青岛即墨区期末]如图,在△ABC中,B60°BC18,点D在边AB上,CACDBD7,则AD的长是    

 <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>

(17)

18[新考向数学文化]勾股定理a2b2c2本身就是一个关于abc的方程,满足这个方程的正整数解(abc)通常叫做勾股数组.毕达哥拉斯学派提出了一个构造勾股数组的公式,根据该公式可以构造出如下勾股数组:(345)(51213)(72425),….分析上面勾股数组可以发现,41×(31)122×(51)243×(71),….分析上面规律,可知第5个勾股数组为    

三、解答题(66)

19(8)请用直尺、圆规作图,不写作法,但要保留作图痕迹.

已知:如图,α,直线ll上两点AB

求作:Rt△ABC,使点C在直线l的上方,且ABC90°BACα

 <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(8)如图,在由边长为1个单位长度的小正方形组成的正方形网格中,点ABC均在正方形网格的格点上.

(1)在图中画出△ABC关于直线l成轴对称的△AB'C'

(2)线段CC'被直线l    

(3)△ABC的面积为    

(4)在直线l上找一点P,使PBPC的长最短.

 <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(8)如图,大正方形是由边长为1的小正方形拼成的,ABCD四个点都是小正方形的顶点,以其中的三个点为顶点构造三角形.

(1)其中一共有    个直角三角形;

(2)请判断△ABC的形状,并说明理由.

 <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(10)[2023·苏州]如图,在△ABC中,ABACAD为△ABC的角平分线.以点A圆心,AD长为半径画弧,与ABAC分别交于点EF,连接DEDF

(1)试说明:△ADE≌△ADF

(2)BAC80°,求BDE的度数.

 <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>



23(10)如图,在△ABC中,ADBC于点DEF垂直平分AC,交AC于点F,交BC于点E,且AEAB

(1)BEA70°,求C的度数;

(2)若△ABC的周长为26cmAC10cm,求DC的长.

 <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>



24(10)如图,在四边形ABCD中,ABADCBCDA60°,点EAD上一点,连接BDCE交于点FCEAB

(1)判断△DEF的形状,并说明理由;

(2)AD12CE8,求CF的长.

 <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(12)[2023·泰安期中新考法建立模型法](1)【模型建立】如图,在Rt△ABCRt△ADE中,ABACADAEBACDAE90°,试说明:△AEC≌△ADB

(2)【模型应用】如图,在△ABC与△ADE中,ABACADAEBAC

DAE90°BDE三点在一条直线上,ACBE交于点F,若点F

AC的中点.

BEC的度数;

CE3,求△AEF的面积.

 <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、1C 2B 3C 4A 5C 6A 7C 8C

9C 【点拨】因为△ABC的三边分别为abc,满足c2a2b2

所以△ABC为直角三角形.

因为c22b20,所以c22b2

所以a2b22b2,所以ab,所以△ABC为等腰直角三角形,所以这个三角形的三个角的度数分别为45°45°90°

10D 【点拨】如图,作BODC于点O

 <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>

由题意得ADBO6mABOD1064(m)

因为DC12m,所以OC8m

所以由勾股定理得BC2BO2OC26282102,所以BC10m

所以大树的高度为106420(m)

故选D

11B 【点拨】因为三角形纸片ABC中,BC

所以ABAC

由折叠可知,BCBECDDEAE2AFDF

所以ABACAFDFCD2AF2

又因为ABAEBE2BC

所以2BC2AF2,所以BC2AF

因为△ABC的周长为13

所以ABACBC13

2AF22AF22AF13,所以AF15

AF的长为15

12A 【点拨】设图中等腰直角三角形的边长为a,图中等腰直角三角形的边长为b,图中等腰直角三角形的边长为c

如图,因为最大正方形的边长为4

所以a2a242

所以第一个等腰直角三角形的面积为 <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> a·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> a24

如图,易知b2b2a2,即2b28

所以图中三个等腰直角三角形的面积和为 <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> a2 <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> b2 <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> b24228

如图,易知c2c2b2,即2c24

所以图中共计7个等腰直角三角形的面积和为 <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> a2 <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> b2 <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> b2 <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> c2 <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> c2 <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> c2 <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> c2422111112

由此推理,第n个图中所有等腰直角三角形的面积和为4n

故选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>

二、13.三角形具有稳定性 144 1524

1665 【点拨】如图,由题意知1α55°

 <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>

2β

3γ75°

因为134180°

所以450°

又因为24β180°,所以β65°

174 【点拨】如图,过点CCEAD,垂足为E

 <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>

所以CEB90°

因为B60°,所以BCE90°B30°

因为BC18,所以BE <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> BC9

又因为BD7,所以DEBEBD2

因为CACDCEAD

所以AD2DE4

18(116061) 【点拨】根据题意可知第4个勾股数组中间的数为4×(91)40,即勾股数组为(94041);第5个勾股数组中间的数为5×(111)60,即勾股数组为(116061)

三、19.【解】如图所示,△ABC为所求作的直角三角形.

 <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>

20.【解】(1)△AB'C'如图所示.

(2)垂直平分

(3)3

(4)P如图所示.

 <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.【解】(1)2

(2)△ABC是直角三角形.理由:

根据题意可得AC212225AB2224220

BC25225,所以AB2AC2BC2

所以△ABC是直角三角形.

22.【解】(1)因为AD是△ABC的角平分线,

所以BADCAD

由题意知AEAF

在△ADE和△ADF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>

所以△ADE≌△ADF(SAS)

(2)因为BAC80°AD为△ABC的角平分线,

所以EAD <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> BAC40°

由题意知AEAD

所以AEDADE

所以ADE <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> ×(180°40°)70°

因为ABACAD为△ABC的角平分线,

所以ADBC,即ADB90°

所以BDE90°ADE20°

23.【解】(1)因为EF垂直平分AC

所以AEEC,所以CCAE

因为BEA70°,所以AEC180°BEA110°

所以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> ×(180°110°)35°

(2)因为△ABC的周长为26cmAC10cm

所以ABBC16cm

所以ABBEEC16cm

因为AEABADBCAEEC

所以BDDEABEC

所以2AB2BD16cm,所以ABBD8cm

所以DCECDEABBD8cm

24.【解】(1)△DEF是等边三角形.

理由:因为ABADA60°

所以△ABD是等边三角形,

所以ABDADB60°

因为CEAB

所以CEDA60°DFEABD60°

所以CEDADBDFE60°

所以△DEF是等边三角形.

(2)连接AC.因为ABADCBCD

所以AC垂直平分BD,即ACBD

又因为ABADBAD60°

所以BACDAC30°

因为CEAB,所以BACACE30°

所以ACECAD30°,所以AECE8

所以DEADAE1284

(1)可知△DEF是等边三角形,

所以EFDE4,所以CFCEEF844

25.【解】(1)因为BACDAE

所以BACEABDAEEAB

所以EACDAB

在△AEC和△ADB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>

所以△AEC≌△ADB(SAS)

(2)因为BACDAE

所以BACCADDAECAD

所以DABEAC

在△AEC和△ADB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>

所以△AEC≌△ADB(SAS)

所以ABEACE

所以BEC180°ACEEACAEB

180°ABEEACAEB

BAC

90°

AGBE于点G,如图所示,

 <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>

因为△AEC≌△ADB,所以BDEC3

因为点FAC的中点,所以AFCF

在△AGF和△CEF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>

所以△AGF≌△CEF(AAS),所以AGEC3

所以SACESABD <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> ×3×345

又因为点FAC中点,

所以SAEF <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> SACE <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> ×45225