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Multiple Choice Questions (MCQs), having same number of sides, polygons, are similar, if, Two, Two polygons, , 1., , Their corresponding sides are proportional, , (a), Their, (C), , (d), , corresponding angles are equal, , None of these, , of the following, , (b) 3 cm (C) 6 cm (d) 9 cm, AABC, it is given that AB= 6 cm,, , em, , In a, AC 8 cm and AD is the, , 7., , bisector of 2A. Then,, , Both (a) and (b), , Which, , (a) 27, , pairs shows similar, , (b) 9: 16, (C), , figures?, , (b), , 8 em, , BD DC=, (a) 3:41, 4:3, , (d) v3:2, 20 cm,, then, , IfAABC~APQR, perimeter of AABC=, perimeter of APQR= 40 cm and PR= 8 cm,, 8., , If AABC~ APQR,, , then what, , are, , the values, , the length of AC is, , (a) 8, , ofr and y?, , cm, , (b), , 6, , cm, , (d), , (c) 4 cm, , 5 cm, , =, 9 cm, BC, In AABC, it is given that AB, is given, 6cm and CA= 7.5 cm. Also, ADEF, such that EF= 8 cm and ADEF~ AABC. Then,, perimeter of ADEF is, , 9., , 12, , 10, , 4, a), , 21 15, , (b), , 2, , 21, , 4., , 15 17, , 2, , ABC and PQR are 60 cm and 36 cm respectively., IfPQ= 9 cm, then AB equals, (a) 6 cm (b) 10 cm (c) 15 cm (d) 24 cm, 11. In the following figure, DE | BC. Find the, value of x., , If AABC ~ APQR, then y+z equals, , 30, , 30 c, , R, , 43, , (a) 2+3, , (b) 4+3v3, , ()4+v3, , (d) 3+4V3, , (a)s, (b) v6, , 12. In the given figure,, if PQ|BC. Find AQ., , Cm, BC= 8cm and PQ=4 cm., then AQ is equal to, , (b), , 4.5 cm, , If, , equal to, , 1, , B, , 2 cm, , Cm, , (c) 9 cm, (d) 9.5 em, , that, 13. Ifin AABC, AB= 6 cm and DE| BC such, , triangle ABCis similar to triangle, , suchthat848AB= DE, , 1, , (d) v7, , 3.5 cm, , 6., , 2x, , 3, , (a), , 2 cmn, 2.5 cm, 3 cm, 3.5 cm, , x+ 4, , (), , . I n the given figure, AACB-AAPQ. If AB=6, , (a), (b), e), (d), , (d) 30 cm, , 10. The perimeters of two similar triangles, , (d) None of these, , (o) 24, , (b) 25 cm, , (a) 22.5 cm, (c) 27 em, , nd BC= 9 cm, then, , DEF, , EFis, , AE=AC, then the length of AD, (a) 2, , cm, , b) 1.2 cm (c), , 1.6, , cm, , is, , (d), , 4, , cm

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60, , In the adjoining figure, DE | BC. The value, of x is, 2x-1, , (d), , be, , 14., , (), , a+b, , BC|\AD and, , such that BCLA, a trapezium, 21. ABCD is, diagonals AC and B[Din, D intersect, AB-4 cm, Ifthe, , 2x+6, , that, , atOsuch, (a), , (b), , 4, , 6, , ac, , a+b, , (d), , c)8, , (a), , 10, , 15. In figure, LM | AB. If AL = x-3, AC= 2x,, , OB, , AO, OC, , 1, , CD =, , OD2hen, , (b) 8 cm (c)9 cm, , 7 cm, , (d) 6 cm, , 22. In the figure, PQ|| BC and AAPQ ~, , BC, , BM=x-2 and BC= 2x +3, find the value of x., (a) 2, , (b), , (a), , (b), , 3, , 8.5, , AD, 16. In figure, it DC, , (c), , BE, , EC and, , BC = AC, , (b) AB =AC, (c), , AB, , (d), , CE = DE, , (d), , 2, , 23. If the ratio of the perimeters of two similar, , 2CDE = LCED, then, (a), , thenis, , 9.5, , (c)9, (d), , BC, , BC, , of the areasot, , triangles is 4: 25, then, the similar triangles is, , the ratio, , (a), , (b) 2:5, (d) 625: 16, , 16: 625, , (c)5:2, 24. Ratio of areas of two similar trianglesis, , 17. Ifin two triangles, corresponding sides are, , 2:3. The ratio of their corresponding sides is, , in the same ratio, then the two triangles are, , (a) 3:2, , (b) V6:1, , c)1:V6, , (d) 2:, , similar. This criterion is known as, , (a) SSS similarity criterion, (b) SAS similarity criterion, (c) AA similarity criterion, (d) AAA similarity criterion., , 25. The areas of two similar triangles are 25 cm, , and 36 cm2. Ifthe median of the smaller triangle is, , 18. If in two similar triangles ABC and DEF,, AB, , BC, , DE, , EF, , then, , 26. The areas of two similar triangles are, , (a) ZB =ZE, , (b), , (c), , (d) 2A = ZF, , B = ZD, , 19. In two, , triangles ABC, , LB = ZF. Then,, , A, , 121 cm and 64 cm respectively. If the median, of the first triangle is 12.1 cm,, then the, , = ZE, , and DEF, LA = ZE and, , is equal to, AC, , (a), , DE, , DF, , 20. In the, , (a), , (b), , (b), , 10 cm, then the median of the larger triangle isS, (a) 12 cm (b) 15 cm () 10 cm (d) 18 cm, , EF, , ED, , (C)ED, , EF, , figure,, , find, , x, , (d), , 4ar(APQR). If BC, , EF, DF, , in terms of a, b and, , (a) 9 cm, 28., c., , L, , ab, , corresponding median of the other triangle is, (a) 11 cm, (b) 8.8 cm, (c) 11.l cm, (d) 8.1 cm, 27. AABC ~APQR such that, ar(AABC), , ac, , B5, ---b------N-----C----- b, , 10 cm (c), , 6 cm, , QR=, (d) 8 cm, , If D, E, Fare the mid-point of sides BC,, , (a) 1:4, MÁ5, , 12 cm, then, , and AB respectively of AABC, then the ratio o, , the areas of, , aa+C, , b+C, , (b), , =, , 43, , triamgles, , (b), , DEF and ABC 1s, 1:2, (c) 2:3 ()0, , In an isosceles triangle ABC, if AC = B, , and AB, , (a) 30°, , =, , 2AC?, then, (b) 45, , 2C is, , equal to, , (c) 90°, , (d) 60

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30., 2C=, , (a), , BC is an, a0°, If BCm, , inosceles, triangle, 4, em,, , 4v2 cm, , ( c ) 4cm, , then find, AB., (b) 2/2 cm, , hich, 39., , (d) 2 emn, , poles of height 13 mand 7, m, tand vertically on, respectively, plane, ground, at a, from each ther., 'The, distance, their tops is, distance between, Two poles, , 31., , e, , 1f ABC, , and BC, , a, , of 8, , (b), , 9 m, , The, , 32., , 10 m, , lengths, , (c) 11, , m, , (d), , of the, , m, , a, , are 24 cm, the rhombus is, , (a), , 12, , diagonals of rhombus, and 10 cm. The, length of each, , 12 cm (b), , side of, , 13, , cm, , (C), , 14 cm, , (d), , 17, , cm, The length ot the, diagonal of a square is, 72 cm. Then, the area of the square, (in cm2) is, (a) 28, (b) 14/2 (c) 21, (d) 49, 24. The lengths of the, diagonals of a rhombus are, 16 cm and 12 cm. Then, the length of the, side, , of the rhombus is, (a) 9 cm, (b) 10 cm (c) 8 cm, , triangles, , CA then, , QR, , 40. Dis, , point on side BC of, LADC, (a) BCx ZBAC,, AD then CA, (C), , AABC, , (c), , ACBA APQR, , (d) ABCA, , APQR, , 41. If AABC, , APQR, AB, perimeter of AABC, perimeter of APQR., and, , (a) 96 cm, (c) 12 cm, , triangles DEF and PQR, ZD =2, is not, and 2R =LE, then which of the following, EF, , DE, , b) PQ, , (d), , QR PQ, , 2x-1 E, , (b), (a), , congruent, , 38. If in, then, , (a), (C), , congruent, , they, , as, , well, , are, , similar, , will be, , 2B = ZE, ZB= ZD, , as, , of a, , AC, , (a) P, , SC, CP, , SC, are, , AABC. AB, , AC, the sides AB and, AE 12 cm, =, 12 cm, AD 8 cm,, , points, , on, , =, , =, , c m . Then, and AC = 18, CE, (a) BD |, DE 1 BC, , (c), , (b), (d), , AD 1 AE, DE, , || BC, , ZF, figure, find, 45. In the given, , 12cm, , A, , similar, , 8 0 3 3 cm, , BC, , F DE FD, , B, , when, , (b)2A=ZD, , (d), , 2A, , =, , LF, , (a), , 60, , 60°, , /7.6 cm, , 6V3 cm, , 3.8 cm/, , DE,, ABC and, , similar,, , ) RA, , similar, , nor, , QR, and CA || SR., , AP, , AB, , 44. D and E, , triangles, , 2/3, , QB, , QR, ZP=2, , (d), , Then, BP, , RP, , AB, , triangles, , c, , x, , b) 3/5 ( ) 3/2, , 5/3, , (C), , congruent, similar but not, , (C)neither, , =, , x+3, , DE, , the, and AB =3 DE. Then,, congruent, , given figure, DE || AB, AD 2x,, =2ax 1 and CE =x. Then, find, 2x, , (a), , RP, , ZB=ZE,, , but not, , 6.5 cm, PQ= 10.4 cm, 60 cm, then find the, , (d) 60 cm, , EF, , DEF,, 37. Intriangles ABC and, two, , (a), , =, , DC = x +3, BE, the value of x., , true?, , DF, , 8 cm, , (b) 100 cm, , 42. In the, , 36. If in two, , PR PQ, , (d), , AABC such that, , a, , 43. In the given figure, BA|, , (b) APQR, , DF, , cm, , (b) BC, (d) BC CD, , AB', , (a), , ACAB, , DE, , () 20, , a, , ABC and PQR,, , APQR, , (c), , cm, , AB=18 cm, , equal to, , (d) 20 cm, , (a), , (a), , 12, , is, , AB= 18cm, , D, , PR P O : e n, , EF, , (6), , then PR, , =, , 33,, , 35. If in two, BC, AB, , AQRP, ar(PQ), ar(ABC), , 15 cm,, , 10 cm, , m, , (a), , =, , 61, , D, (d), , 6 cm, , (b), , 80°, , (c), , 40, , 100°

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46. E is, , point on the side AD produced of a, parallelogram ABCD and BE intersects CD at, a, , 53. In, , given figure,PQ || BC. Find AB in, , F. Then, , (a) ACFB ABAE, , (C)AABE ABFC, , (d) ACFB, , P, , AAEB, , cm, , 47. In the given figure, PB and QA are, , B, , perpendiculars to segment AB. If PO = 5 cm,, Q0= 6 cm and ar(APOB) = 125 cm2, then find, the area of AQOA., O, , (a), , 48. A, , (a), , 7 m, , (b), , 17 m, , (c), , 7B, , PQ I| AB, , (b), , PQ = AB, , x+3, (a), , 1, , (b), , (d) AD= AC, , (a), (c), , 2 cm, 3 cm, , 57. In, , PM, , =, , 6, , (b) 100 cm, , B4, , 5 cm, 8 cm, , 4 cm D 2 cm, , ALMN, PQ| MN such that LP= 2 cm and, cm. Also MN, 20 cm. Find PQ (in cm)., =, , such that ZB, , ar(APQR), , (b), , 25, , if BC, , (c) 2500, , =, , (a), , 2, , cm, PA, , (b), , 3, , N, , 20 cm, , (d) 5, (c) 4, BC 4, EF=5 cm and, AABC =64 cm2, find cm,., the area of EF, (a) 100 cm2, (b) 75 cm, (c) 50 cm, (d) 125 cm, 59. In AABC, BC, and APQR, ZB=, LQ and AB, , 58., , If AABC ADEF,, area of, , If ar(AABC), , (d) 80 cmn2, , If AABC APQR, =ZR, find a, 5, , 6 cm, , M, , 150 cm2, 200 cm2, , QR = 7 cm., , (a), , (d) 4, , 6 cm, , DE, , 2C, , (b), (d), , 2, , 51. In the given, =, figure, DE|| BC. If, 4 cm,, BC =8 cm and area of AADE = 25, cm., sq., Find, the area of AABC., , 52., , (c) 3, , determine AC., , (d PQ=AC, , (c), , 2, , 56. In the figure, AD is the, bisector of 2A. If BD = 4 cm,, DC = 2 cm and AB = 6, cm,, , (c)PQI| CD, , (a), , 3x+4, , 3ax+19, , (d) 23 m, , 50. In the given figure, D and E are two, points, lying on side AB, such that AD = BE. If DP||BC, and EQ || AC, then, , (a), , will make DE || AB in the, , r, , figure?, , (b) DE || BC, , DE = BC, , B, , (b) 4.8 cm, , 55. What values of, , 49. In AABC, D and E are, points on sides AB and, AC respectively such that BD = CE. If ZB, =2C,, , then, (a) AE || BD, , E, , (d) 3.5 cm, , point., , (c), , (d) 6, , 13.5 cm,, , =, , 5.8 cm, , m, , 15 m, , (c) 4, , 54. In the adjoining figure,, DE| BC. If AD =3.4 cm, AB, , due west and then 8 m, due north. Find the shortest distance between, his starting point and ending, man, , 5, , =, , (b) 150 cm, (d) 180 cm2, goes 15, , (b), , 2, , (c), , ()200 cm, , 6 cm, , 8.5 cm and AC, find AE., (a) 5.4 cm, , 6cm, , (a) 100 cm2, , 2 cm, , 2.4 cm, , (b) AABE ACFB, , cm)., , =, , po QR, , 16, , ar(APQR) and BC =8 cm, then find, , =, , 3.5, , 2Q, m, , and, , (a) 9 cm, , and, , 60. A, ladder is, foot is at a, , tip reaches, , (d) 50, , b), , 8 cm, , (C)5 cm, , placed in such a, distance of 7 m from a way, , 24, Determine thewindow, length of, , (a) 13 m, , (d) 6 cm, , w, , a, , (b), , 18 m, , m, , the, , (C), , above tu, , ladder, , 25, , m, , (d), , ts, , rQund, , gro, 30, , m

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20., , 2(12.1)x64, , (b): In AKNP and AKMIL, , (Given), , KNP- ZKML=35, K, , (Common), , K, , (By AA similarity criterion), , AKNP AKML, PN, LM, , KN, KM, , KN+ NM, , x 8.8., , 27. (c):Since AABC~APQR, , aC, , C, , C+b, , = 77 44, , 121, , 64, , ar(AABC), , *b+C, , 21. (b): In AAOB and ACOD, we have, , 4ar(APOR) 122, , BC, , ar(APQR) OR?, , ar(APQR) QR, :, , Given, ar(AABC) = 4ar(APQR), , LAOB 2COD, , OC, , (By SAS similarity criterion), , AAOB ACOD, , OC, , = 36, , QR = 6, , cm, , 4, , AOO-(Given), CD, , 144, , QR =, , (Vertically opposite angles), , CD 2, , CD, , =, , 28. (a): We know that the line segment joíning the, mid-points of two sides of the triangle is half the length, of the third side., , 8 cm, , 22 (b):Given, AAPQ AABC, , AP PO, A AP+PAB, , BC, , Given,, , AB, , AP, , ), DE-AB, EF -BC and DF-AC, , 1 AP 2, , AP, , 23. (a): Let AABC, , APQR., , DE EF, , DF, , AB, , AC, , Thus, ADEF ~ AABC (By SSS similarity criterion), , Since, ratio of areas of two similar triangles is equal to, the square of the ratio of any two corresponding sides., , ar(APQR), , PQ, , 29. (c): We have, AC BC, and AB = 2AC = AC2+ AC2, , (Perimeter of AABC, , -, , AB =BC2+ AC?, , Perimeter of APQR, 24., is, , ar(ADEF)=, -ar(AABC), , 2, , Then, arAABC), , BC, , [: AC =BC], , (d): Since, ratio of the areas of two similar triangles, , equal to the square of the ratio of their corresponding, , sides., , By, , converse of, , theorem, 2C = 90°, , Pythagoras, , 30., , Square, , of ratio of, , corresponding, , sides, , =, , (a): Given, AABC is an, isosceles triangle and 2C, 90°, A C BC =4 cm, AB is the, longest side., =, , =, , Ratio of the, , corresponding sides, , =, , 2, , In AABC,, , ., , 25. (a): Let the median of the, larger triangle be x cm., We know, the ratio of the areas of two similar, triangles, is equal to the square of the ratio of their, corresponding, medians., , 2= 100x36, 25, , = 144 x= 12, , 26. (b): Let the, corresponding median of the other, triangle be x cm., As the ratio of the areas of two, similar, is, equal to the square of the ratio of their, corresponding, mediansS., , triangles, , Cm, , AB AC+ BC2, AB 42 42 =16 +, =, , AB, 31., , =, , +, , (6): Let, , BE, In, , =, , 6, , m, , 32, cm, , AB and CD be the, =, , 7, , m, , and CA =8 m., , poles, , suct, , that, , L AB., , CD =7 m,, and DE, 8 m., , =, , =, , right ABDE, by, , theoremn, , 16, , 32= 16 x2 4/2, , AB 13 m, CD, , Draw DE, Then, AE, , (By Pythagoras theorem, , Pythagoras, , Df-----a8, , AE, D, , m, , 8 m