2022年九年级数学相似三角形练习题及答案 .pdf

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1、relationship, establishe d equivalent relationship 14, and subject: application problem (4)-scores and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associa

2、te volume rate corresponds to relationship, Then in-li ne solution. Category fraction multiplication w ord problem score Divisi on appli cations engineering pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of me

3、asurement and their significance in rate 1, curre ncy, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units a nd their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method

4、 of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)-line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry pr

5、eliminary knowledge (2)-plane graphics review content triangle, and edges shape d, and round, and fan axisymmetric graphi cs perimeter and area combination graphics of area subject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column

6、is divided i nto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship betwee n characteristics of circular cone is slightly solid surface area and volume 1, size 2, table .和相似三角形练习题1、如图，当四边形PABN的周长最小时，a2、如图，已知等腰三角形 ABC 的边 AB长为 2 ，DE是它的中位线，则下面四个结论：（1）DE=1 ， （2）CDECAB,(3) CDE

7、的面积与CAB面积之比为1：4，其中正确的有（）2题图EDCBA(3题图）EDCBAA、 0 个 B、1 个 C 、2 个 D 、3 个3、如图（ 3） ，等腰ABC中，底边 BC=a,A=036,ABC的平分线交AC于 D，BCD的平分线交BD于 E，设512k，则 DE=( ) A、2K a B 、3K a C 、2ak D 、3ak4、已知 : ABC与DFE相似且面积比为4： 25，则ABC与DFE的相似比为。5、（20XX年滨州）如图所示，给出下列条件： BACD； A D CA C B； A CA BC DB C； 2A CA DA B其中单独能够判定ABCACD的个数为（）A 1

8、 B2 C3 D4 （5 题图） （6 题图）6、20XX年上海市 ) 如图，已知ABCDEF，那么下列结论正确的是（）A ADBCDFCEBBCDFCEADCCDBCEFBEDCDADEFAF7、(2009 成都 ) 已知 ABC DEF ，且AB ：DE=1 ：2，则 ABC的面积与 DEF 的面积之比为 (A)1：2 (B)1：4 (C)2：1 (D)4：1 8、 （2009 重庆綦江）若ABC DEF, ABC与 DEF的相似比为2，则 ABC与 DEF的周长比为（）A 14 B12 C21 D29、 （20XX 年杭州市）如果一个直角三角形的两条边长分别是6 和 8，另一个与它相似的

9、直角三角形边长分别是3和 4 及x，那么x的值（）y x P(a，0) N(a+2，0) A(1，-3) （1 题图）B(4，-1) O 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: application problem (4)-scores and perce ntage application problem review content overview answ ers scores,

10、 and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associate volume rate corresponds to relationship, Then in-li ne solution. Category fraction multiplication w ord problem score Divisi on appli cations engineering pr oblem problem X

11、V, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, curre ncy, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units a nd their relationships

12、. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)-li ne and angle review content lin

13、e, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)-plane graphics review content triangle, and edges shape d, and round, and fan axisymmetric graphi cs perimeter and area combination graphics of area s

14、ubject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided i nto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship bet ween characteristics of circular cone is slightly solid surface area and v

15、olume 1, size 2, table .和A 只有 1 个 B可以有2 个 C有 2 个以上但有限 D有无数个10、(20XX 年宁波市） 如图，菱形ABCD中，对角线AC、BD相交于点O，M、N分别是边AB、AD的中点，连接OM、ON、MN，则下列叙述正确的是（）A AOM和AON都是等边三角形B 四边形MBON和四边形MODN都是菱形C 四边形AMON与四边形ABCD是位似图形D 四边形MBCO和四边形NDCO都是等腰梯形11、 （20XX年江苏省）如图，在5 5方格纸中，将图中的三角形甲平移到图中所示的位置，与三角形乙拼成一个矩形，那么，下面的平移方法中，正确的是（）A 先向下平

16、移3 格，再向右平移1 格B 先向下平移2 格，再向右平移1 格C 先向下平移2 格，再向右平移2 格D 先向下平移3 格，再向右平移2 格(11 题图 ) （13 题图）12、(20XX 年义乌 ) 在中华经典美文阅读中，小明同学发现自己的一本书的宽与长之比为黄金比。已知这本书的长为 20cm，则它的宽约为A 12.36cm B.13.6cm C.32.36cm D.7.64cm 13、 （20XX年娄底）小明在一次军事夏令营活动中，进行打靶训练，在用枪瞄准目标点B时，要使眼睛O 、准星 A、目标 B在同一条直线上， 如图 4 所示，在射击时， 小明有轻微的抖动，致使准星A偏离到 A，若 O

17、A=0.2 米，OB=40米 ， AA =0.0015米 ， 则 小 明 射 击 到 的 点B 偏 离 目 标 点B的 长 度BB 为（）A3 米B0.3 米C 0.03 米D0.2 14、20XX年孝感）如图，将放置于平面直角坐标系中的三角板AOB绕O点顺时针旋转90得AOB 已知D B C A N M O 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: application problem

18、(4)-scores and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associate volume rate corresponds to relationship, Then in-li ne solution. Category fraction mu

19、ltiplication w ord problem score Divisi on appli cations engineering pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, curre ncy, length, area, volume, unit size,

20、volume, weight and rate. (Omitted) 2, commonly used time units a nd their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates

21、 16, and subject: geometry preliminary knowledge (1)-li ne and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)-plane graphics review content triangle, and edges shape d, and

22、round, and fan axisymmetric graphi cs perimeter and area combination graphics of area subject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided i nto: cuboid, square 3, cone cone of the features of cuboids and cubes rela

23、tionship betwee n characteristics of circular cone is slightly solid surface area and volume 1, size 2, table .和AOB=30，B=90，AB=1，则B点的坐标为 ( ) A 3 3()22B33()22 C13()22 D 3 1(,)2215、 （ 20XX 年天津市）在ABC和DEF中，22ABDEACDFAD，如果ABC的周长是16，面积是12，那么DEF的周长、面积依次为（）A 8，3 B 8，6 C4，3 D ， 6 16、 （20XX年新疆）如图，小正方形的边长均为1，则

24、下列图中的三角形（阴影部分）与ABC相似的是（）17、( 内江市 2010) 如图，梯形ABCD中，ADBC，点E在BC上，AEBE，点F是CD的中点，且AFAB，若2.746ADAFAB，则CE的长为A 2 2 B. 2 31 C. 2.5 D. 2.3(17 题图 )FEDCBA18、 （内江市2010）如图，在ABC中，ABAC，点EF、分别在AB和AC上，CE与BF相交于点D，若AECFD，为BF的中点，AEAF的值为 _. 19、在ABC中，D、E分别是 AB 、AC的中点连结DE 、BE 、CD ，且 BE与 CD交于点 O ，若DEO的面积DEOS=1,则ABC的面积ABCS=

25、。20、如图，在ABC，点D、E 分别在AB、AC 上，连结DE 并延长交BC 的延长线于点F，连结DC 、BE，若0180BDEBCE。 （ 1 ） 请 写 出 图 中 的 两 对 相 似 三 角 形 ;( 不 另 外 添 加 字 母 和 线 ) 。 （ 2） 任 选 其A.（18 题图）精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: application problem (4)-scores

26、 and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associate volume rate corresponds to relationship, Then in-li ne solution. Category fraction multiplicati

27、on w ord problem score Divisi on appli cations engineering pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, curre ncy, length, area, volume, unit size, volume, we

28、ight and rate. (Omitted) 2, commonly used time units a nd their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and s

29、ubject: geometry preliminary knowledge (1)-li ne and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)-plane graphics review content triangle, and edges shape d, and round, and

30、 fan axisymmetric graphi cs perimeter and area combination graphics of area subject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided i nto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship b

31、et ween characteristics of circular cone is slightly solid surface area and volume 1, size 2, table .和中一对进行证明。 （20 题图）DEFCBAOFECBA（ 19 题图）21、小曼和他的同学组成了“爱琢磨”学习小组，有一次，他们碰到这样一道题：“已知正方形ABCD ，点 E 、F、G 、H分别在边AB 、BC 、CD 、DA上，若EGFH，则 EG=FH 。 ”为了解决这个问题，经过思考，大家给出了以下两个方案：方案一：过点A作 AM/HF 交 BC于点 M ，过点 B作 BN/EG 交

32、CD于点 N；方案二：过点A作 AM/HF 交 BC于点 M ，过点 A作 AN/EG 交 CD于点 N 。, (1) 对小曼遇到的问题，请在甲、乙两个方案中任选一个加以证明（如图（1） ） ；（2）如果把条件中的“正方形”改为“长方形”，并设AB=2,BC=3 （如图（ 2） ） ，是探究EG 、FH 之间有怎样的数量关系，并证明你的结论；（3） 如果把条件中的 “EGFH” 改为“ EG与 FH的夹角为045” ， 并假设正方形ABCD的边长为 1， FH的长为52（如图（ 3） ） ，试求 EG的长度。图（ 3）图（ 2）图(1)HDGCFBEAEAHDGFCBEGHDCFBA22、如图

33、， E 是ABCD的边 BA延长线上一点，连接EC ，交 AD于 F。 （1）写出图中的三对相似三角形（注意：不添加辅助线） ； （2）请在你所找出的相似三角形中选一对，说明相似的理由。FEADCB（22 题图）EFADCB（23 题图）23、如图，已知ABC，延长 BC到 D，使 CD=BC 取 AB的中点 F,连接 FD交 AC于点 E。精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: appl

34、ication problem (4)-scores and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associate volume rate corresponds to relationship, Then in-li ne solution. Cate

35、gory fraction multiplication w ord problem score Divisi on appli cations engineering pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, curre ncy, length, area, vol

36、ume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units a nd their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement

37、2, and estimates 16, and subject: geometry preliminary knowledge (1)-li ne and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)-plane graphics review content triangle, and edg

38、es shape d, and round, and fan axisymmetric graphi cs perimeter and area combination graphics of area subject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided i nto: cuboid, square 3, cone cone of the features of cuboid

39、s and cubes relationship betwee n characteristics of circular cone is slightly solid surface area and volume 1, size 2, table .和（1）求AEAC的值；（2）若 AB=a，FB=EC ，求 AC的长。24、(20XX 年梅州市 )如图，梯形ABCD中，ABCD，点F在BC上，连DF与AB的延长线交于点G （1）求 证 ：C D FB G F；（ 2 ） 当 点F是BC的 中 点 时 ， 过F作EFCD交AD于 点E， 若6 c m4 c mA BE F，求CD的长相似形

40、练习参考答案1、47 2、D 3 、 A 4 、2：5 5 、C 6 、A 7 、B 8 、B 9 、B 10 、C 11 、D 12 、 A 13 、 B 14、A 15 、A 16 、A 17 、D 18 、512 19 、12 20 解： （1）FDBFCE; ABCAED (2)证明：FDBFCEFF,180,18000又ECFBDEECFBCEBCEBDEFDBFCE( 有两对角对应相等的两个三角形相似) 21、(1) 证明：过点A作 AM/HF 交 BC于点 M,作 AN/EG 交 CD的延长线于点N ，AM=HF,AN=BC, ,1 分。在正方形ABCD 中， AB=AD090A

41、DNBADABM090,NAMFHEG,DANBAM,3 分，在中和ADNABM，ABMADNABMADABDANBAM,ADNFHEC,即ANAMNGEBCMFHANDGCFMBEHAEPBMFCGNDHA（1）（2）（3）（2）结论： EG ：FH=3 ： 2 D C F E A B G 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: application problem (4)-score

42、s and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units 1) (2) find associate volume rate corresponds to relationship, Then in-li ne solution. Category fraction multiplicat

43、ion w ord problem score Divisi on appli cations engineering pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, curre ncy, length, area, volume, unit size, volume, w

44、eight and rate. (Omitted) 2, commonly used time units a nd their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and

45、subject: geometry preliminary knowledge (1)-li ne and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)-plane graphics review content triangle, and edges shape d, and round, an

46、d fan axisymmetric graphi cs perimeter and area combination graphics of area subject : Preliminary knowl edge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided i nto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship

47、bet ween characteristics of circular cone is slightly solid surface area and volume 1, size 2, table .和证明：过点 A作 AM/HF 交 BC于点 M,作 AN/EC 交 CD的延长线于点N，,ECANHFAM在长方形ABCD中， BC=AD,090ADNBADABM,90,0NAMFHEGABMDANBAM.ADN,8 分。ADABANAM,AB=2,BC=AD=3, 23FHEC,9 分。（3）解：过点A作 AM/HF 交 BC于点 M ，过点 A作 AN/EG 交 CD于点 N，25,

48、1FHAMAB. 在ABMRt中， BM=21,10 分。将AND绕点 A顺时针旋转090到APB. 045FHEG的夹角为与，045MAN,045MABDAN,045MANPAM即, 从而ANMAPM,PM=NM. ,12 分。设 DN=x ，则 NC=1-x，MN=PM=x21。在CMNRt中，22)1(41)21(xx解得31x,13 分。31012xANEG。22、解：（1）EAFEBC,CDFEBC,CDFEAF,3 分。（2）选EAFEBC，理由如下：在ABCD中 AD/BC, ,4 分。BEAF。,5 分EE又,6 分，EAFEBC,7 分。23、解：（1）过点F 作 FM/AC

49、，交 BC于点 M ，F 为 AB的中点，M为 BC的中点， FM=21AC ，由 FM/AC，得,FMDECDMFDCEDFMD,ECD32FMECDMDC, 3231,31213232ACACACACECACACAEACACFMEC. (2),2121,aABFBaAB又 FB=EC ，aEC21。.233,31aECACACEC24、 （1）证明：梯形ABCD，ABCD，CDFFGBDCFGBF，CDFBGF（2） 由（ 1）CDFBGF，又F是BC的中点，BFFCCDFBGF，DFFGCDBG，又EFCD，ABCD，EFAG，得2EFBGABBG22462BGEFAB，精选学习资料 -

50、 - - - - - - - - 名师归纳总结 - - - - - - -第 6 页，共 7 页relationship, establishe d equivalent relationship 14, and subject: application problem (4)-scores and perce ntage application problem review content overview answ ers scores, and percentage application problem of key is: according to meaning, (1) dete