2022年九年级数学相似三角形练习题及答案.docx

精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge ge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4)phi cs perimeter and area nd perce ntage applicati combination g on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes arccordi e divide ng to meani ni o: cyli ng, (1) determine standard vol nd cone 2, column is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboido" relationshi i cubes relati p, Then in-li ne soluti betwee n characteristi Category fraction multi cs of circular plicti cone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd vol ppli cations e ume 1, size 2, table . . ng 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, weight and rate. (Omitted) 2, commonly used time units a nd t heir relationships. (Slightly) with a measurement units Zhi jian 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 a nd 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 相似三角形练习题1、如图，当四边形PABN 的周长最小时，a个结论：）2、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（1）DE=1，（2）CDE CAB ,(3) CDE 的面积与CAB 面积之比为1：4，其中正确的有（y ACO P(a，0) N(a+2，0) x BD于 E，设B(4，-1) DEA(1，-3) EDA2题图B（1 题图）B(3题图）CA、 0 个 B、1 个 C 、2 个 D 、3 个3、如图（ 3），等腰ABC 中，底边 BC=a ,A =0 36 ,ABC 的平分线交AC于 D，BCD 的平分线交k51，则 DE=( ) A、2 K a B 、3 K a C 、a D 、3a k2k22ADAB4、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 ；ADCACB；AC CDAB；ACBC其中单独能够判定ABCACD的个数为（）A1 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（）3第 1 页，共 7 页AAD DFBCBBC CEDFCCD EFBCDCD EFADCEADBEAF7、(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（A14 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，另一个与它相似的直角三角形边长分别是和 4 及 x，那么 x 的值（）名师归纳总结 - - - - - - -精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge ge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4)phi cs perimeter and area nd perce ntage applicati combination g on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes arccordi e divide ng to meani ni o: cyli ng, (1) determine standard vol nd cone 2, column is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboids and o" relationshi i cubes relati p, Then in-li ne soluti bet ween characteristi Category fraction multi cs of circular plicaticone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd vol ppli cations e ume 1, size 2, table . . ng pr oblem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of meas s urement 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 t heir relationships. (Slightly) with a measurement units Zhi jian 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)-line 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 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OM、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A B M O N D C 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A12.36cm 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 OA=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（）AOB绕 O点顺时针旋转90° 得 AOB已知A3 米B0.3 米C0.03 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名师归纳总结 第 2 页，共 7 页- - - - - - -精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge ge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4)phi cs perimeter and area nd perce ntage applicati combination graphics on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes arccordi e divide ng to meani ni o: cyli ng, (1) determine standard vol nd cone 2, column is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboido" relationshi i cubes relati p, Then in-li ne soluti betwee n characteristi Category fraction multi cs of circular plicti cone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd volume 1, size 2, table . ngineering 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, weight and rate. (Omitted) 2, commonly used time units a nd t heir relationships. (Slightly) with a measurement units Zhi jian 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)-line 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 AOB=30° ， B=90° ， AB=1，则 B点的坐标为 ( ) A(3 3)B(33) C(13) D (3 1 ,2 2)D，如果ABC的周长是22222215、（ 20XX 年天津市）在ABC和DEF中，AB2 DE，AC2DF，AABC16，面积是 12，那么DEF的周长、面积依次为（）A8，3 B 8，6 C4，3 D， 6 相似的是（）16、（20XX年新疆）如图，小正方形的边长均为1，则下列图中的三角形（阴影部分）与A.17、( 内江市 2010) 如图，梯形 ABCD 中， ADBC，点 E 在 BC 上， AE BE，点 F 是 CD 的中点，且AF AB，若 AD 2.7，AF 4，AB 6，则 CE 的长为A 2 2 B. 2 3 1 C. 2.5 D. 2.3A DF(17 题图 )BEC（18 题图）18、（内江市 2010）如图，在ABC 中， AB AC，点 E、F 分别在 AB 和 AC 上， CE 与 BF 相交于点 D，若AE CF，D 为BF的中点，AE AF 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 S DEO =1,则 ABC 的面积 S ABC = 。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0BDE BCE 180。（ 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 其名师归纳总结 第 3 页，共 7 页- - - - - - -精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge ge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4)phi cs perimeter and area nd perce ntage applicati combination g on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes arccordi e divide ng to meani ni o: cyli ng, (1) determine standard vol nd cone 2, column is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboids and o" relationshi i cubes relati p, Then in-li ne soluti bet ween characteristi Category fraction multi cs of circular plicti cone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd vol ppli cations e ume 1, size 2, table .ng pr oblem probl l em 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, weight and rate. (Omitted) 2, commonly used time units a nd t heir relationships. (Slightly) with a measurement units Zhi jian 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)-line 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 AA（ 19 题图）DEFEO中一对进行证明。 （20 题图）BCFBC21、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 EG 方案：FH ，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一：过点 A 作 AM/HF 交 BC于点 M，过点 B作 BN/EG 交 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0 45 ” ，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。22、如图， E 是AHDAHDAHDGGEEEGCBFCBFCBF图 (1)图（ 2）图（ 3）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。EAFDFAE第 4 页，共 7 页BC（22 题图）BCD（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。名师归纳总结 - - - - - - -精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4) phi cs perimeter and area nd perce ntage applicati combination graphics on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes ar ccordi e divide ng to meani o: cyli ng, (1) determine standard vol nd cone 2, colum n is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboid o" relationshi cubes relati p, Then i n-li ne soluti betwee n characteristi Category fraction multi cs of circular plicati cone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd volume 1, size 2, table . ngineeri ng pr oblem probl em XV, a su bje ct: review of the measur ement of the am ount of capacity, measureme nt and units of measurement of common unit s of measureme nt and their significa nce in rate 1, curre ncy, lengt h, area, volume, unit size, vol ume, weight a nd rate. ( Omitted) 2, commonly used time units a nd t heir relationships. (Slightly) with a measur ement units Zhi jian of of poly 1, and of method 2, a nd poly method 3, and of me thod a nd poly met hod of relationshi p measurement di stance of method 1, a nd t ool measurement 2, and estimates 16, and subje ct: geometry pr eliminary knowle dge (1)-line a nd a ngle review conte nt line, and segme nt, and Ray, and vertical , and parallel, and angle a ngle of classificati on (slig htly) 17, and subje ct: geometry preliminary k nowle dge (2)-plane （1）求AE 的值；（2）若 AB=a ，FB=EC，求 AC的长。AC24、(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D C E F A B G A B 6 c m，E F 4 c m，求 CD 的长相似形练习参考答案1、7 2 4、D 3 、 A 4 、2：5 5 、C 6 、A 7 、B 8 、B 9 、B 10 、C 11 、D 12 、 A 13 、 B 014、A 15 、A 16 、A 17 、D 18 、51 19 、12 220 解：（1）FDB FCE ; ABC AED (2)证明：FDB FCEBDEBCE0 180,BCEECF0 180,BDEECF,又FFFDB FCE ( 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=ADABMBADADN90EGFH,NAM900,BAMDAN,3 分，在ABM和ADN中，BAMDAN,ABAD,ABMADNABMADNAMAN,即ECFHNNEAHFGAHFDPABHM FDGNEBMCEMC（3）GCB（2）（1）（2）结论： EG：FH=3： 2 名师归纳总结 - - - - - - -第 5 页，共 7 页精选学习资料 - - - - - - - - - graphics review content tria she d equivalent relati nd edge onshi s shape d, and round, a nd subject: nd fan axisymmetric gra oblem (4) phi cs perimeter and area nd perce ntage applicati combination g on problem review conte of area subject nt overview : Preliminary k answ ers scores, nowl edge (3)-review and percentage a of soli ppli d content categ cation problem of key is: a ory 1-d shapes ar ccordi e divide ng to meani o: cyli ng, (1) determine standard vol nd cone 2, colum n is divi ume (unit ded i nto: cuboi s "1") (2) find associate "volume rate corresponds t of the features of cuboids and o" relationshi cubes relati p, Then i n-li ne soluti bet ween characteristi Category fraction multi cs of circular plicati cone is slig on w ord pr htly soli oblem d surface area a e Divisi on a nd vol ppli cations e ume 1, size 2, table . ng pr oblem probl em XV, a subje ct: review of the measur ement of the am ount of capacity, measureme nt and units of meas ure