EduSahara™ Assignment
Name : Similarity of Triangles
Chapter : Similarity of Triangles
Grade : ICSE Grade X
License : Non Commercial Use
Question 1
1.
Identify the property by which the two given triangles are similar
  • (i)
    SAS Similarity
  • (ii)
    SSS Similarity
  • (iii)
    not similar
  • (iv)
    AAA Similarity
Question 2
2.
Identify the property by which the two given triangles are similar
  • (i)
    SAS Similarity
  • (ii)
    SSS Similarity
  • (iii)
    AAA Similarity
  • (iv)
    not similar
Question 3
3.
Identify the property by which the two given triangles are similar
  • (i)
    not similar
  • (ii)
    SAS Similarity
  • (iii)
    AAA Similarity
  • (iv)
    SSS Similarity
Question 4
4.
    • In the given figure, △GHI and △QRS are such that
    • ∠H
    • =
    • ∠R
    •  
    • and
    • GH

      QR
    • =
    • HI

      RS
    • .
    • Identify the property by which the two triangles are similar
  • (i)
    SAS Similarity
  • (ii)
    not similar
  • (iii)
    AAA Similarity
  • (iv)
    SSS Similarity
Question 5
5.
    • In the given figure, △ABC and △PQR are such that
    • ∠B
    • =
    • ∠Q
    •  
    • and
    •  
    • ∠C
    • =
    • ∠R
    • .
    • Identify the property by which the two triangles are similar
  • (i)
    not similar
  • (ii)
    AAA Similarity
  • (iii)
    SAS Similarity
  • (iv)
    SSS Similarity
Question 6
6.
    • In the given figure, △FGH and △UVW are such that
    • FG

      UV
    • =
    • GH

      VW
    • =
    • HF

      WU
    • .
    • Identify the property by which the two triangles are similar
  • (i)
    not similar
  • (ii)
    SSS Similarity
  • (iii)
    SAS Similarity
  • (iv)
    AAA Similarity
Question 7
7.
    • In the given figure,
    •  
    • MN
    • KL
    • .
    • If
    •  
    • JM

      MK
    • =
    • 4

      5
    • and
    • JL
    • =
    • 13.7 cm
    • , find
    • JN
  • (i)
    8.09 cm
  • (ii)
    4.09 cm
  • (iii)
    6.09 cm
  • (iv)
    5.09 cm
  • (v)
    7.09 cm
Question 8
8.
    • In the given figure,
    •  
    • HI
    • FG
    • .
    • If
    •  
    • EH
    • =
    • 5.85 cm
    • ,
    • EF
    • =
    • 11.7 cm
    • and
    • EG
    • =
    • 13.3 cm
    • , find
    • EI
  • (i)
    8.65 cm
  • (ii)
    6.65 cm
  • (iii)
    7.65 cm
  • (iv)
    4.65 cm
  • (v)
    5.65 cm
Question 9
9.
In the given figure, PQ ∥ EF and DQ = 13.2 cm, PQ = 12 cm and EF = 20 cm, find DF
  • (i)
    23.0 cm
  • (ii)
    21.0 cm
  • (iii)
    22.0 cm
  • (iv)
    20.0 cm
  • (v)
    24.0 cm
Question 10
10.
In the given figure, △BCD is isosceles right-angled at C and CE ⟂ DB. ∠E =
  • (i)
    ∠B
  • (ii)
    ∠C
  • (iii)
    ∠G
  • (iv)
    ∠F
  • (v)
    ∠D
Question 11
11.
In the given figure, △GHI is isosceles right-angled at H and HJ ⟂ IG. ∠HJG =
  • (i)
    ∠JHI
  • (ii)
    ∠HIJ
  • (iii)
    ∠GHI
  • (iv)
    ∠GHJ
  • (v)
    ∠JGH
Question 12
12.
    • In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
    • Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
    • △FDA ∼
  • (i)
    △ABH
  • (ii)
    △DAE
  • (iii)
    △FEH
  • (iv)
    △DCF
  • (v)
    △ACF
Question 13
13.
    • In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
    • Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
    • ∠AFD  =
  • (i)
    ∠FDA
  • (ii)
    ∠HFE
  • (iii)
    ∠FAC
  • (iv)
    ∠FEH
  • (v)
    ∠HAB
Question 14
14.
    • In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
    • Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
    • ∠ACF  =
  • (i)
    ∠FDA
  • (ii)
    ∠EHF
  • (iii)
    ∠ABH
  • (iv)
    ∠FEH
  • (v)
    ∠DAF
Question 15
15.
    • In the given figure, three lines l , m and n are such that l ∥ m ∥ n.
    • Two transversals PQ and RS intersect them at the points A , B , C and D , E , F respectively.
    • ∠CFA  =
  • (i)
    ∠BHA
  • (ii)
    ∠EHF
  • (iii)
    ∠DAF
  • (iv)
    ∠HFE
  • (v)
    ∠AFD
Question 16
16.
    • In the given figure, MNOP is a trapezium in which
    • MN ∥ OP
    • and the diagonals
    • NP
    • and
    • MO
    • intersect at
    • Q
    • .
    • If
    •  
    • QM
    • =
    • (
      2
      x
      +
      28
      )
    • cm,
    • NQ
    • =
    • (
      2
      x
      +
      19
      )
    • cm,
    • QO
    • =
    • (
      x
      +
      5
      )
    • cm and
    • PQ
    • =
    • (
      x
      +
      1
      )
    • cm, find the value of x
  • (i)
    (
    67
    ,
    66
    )
  • (ii)
    (
    70
    ,
    67
    )
  • (iii)
    (
    68
    ,
    68
    )
  • (iv)
    (
    69
    ,
    69
    )
  • (v)
    (
    67
    ,
    67
    )
Question 17
17.
    • In the given figure, FGHI is a trapezium in which
    • FG ∥ HI
    • and the diagonals
    • GI
    • and
    • FH
    • intersect at
    • J
    • .
    • △JHI
    •  
  • (i)
    △JGH
  • (ii)
    △JFG
  • (iii)
    △JIF
  • (iv)
    △GHI
  • (v)
    △IFG
Question 18
18.
In the given figure, the altitudes PH and IQ of △GHI meet at O. △QHI ∼
  • (i)
    △OHI
  • (ii)
    △QHO
  • (iii)
    △PIO
  • (iv)
    △PIH
  • (v)
    △OQP
Question 19
19.
In the given figure, the altitudes ND and EO of △CDE meet at M. ∠MEN  =
  • (i)
    ∠ENM
  • (ii)
    ∠DMO
  • (iii)
    ∠ODM
  • (iv)
    ∠NME
  • (v)
    ∠MOD
Question 20
20.
    • In the given figure, RS ∥ HI , and median GJ bisects RS.
    • If  GJ = 18.1 cm, GR = 9 cm and GK = 9.05 cm,  GH =
  • (i)
    19.00 cm
  • (ii)
    20.00 cm
  • (iii)
    16.00 cm
  • (iv)
    17.00 cm
  • (v)
    18.00 cm
Question 21
21.
    • In the given figure, RS ∥ JK , and median IL bisects RS.
    • If  IL = 13.8 cm, IK = 17 cm and IM = 4.6 cm,  IS =
  • (i)
    3.67 cm
  • (ii)
    5.67 cm
  • (iii)
    6.67 cm
  • (iv)
    7.67 cm
  • (v)
    4.67 cm
Question 22
22.
    • In the given figure, RS ∥ IJ , and median HK bisects RS.
    •  
    • △HLS ∼
  • (i)
    △HKJ
  • (ii)
    △IJH
  • (iii)
    △HIJ
  • (iv)
    △HIK
  • (v)
    △HRL
Question 23
23.
In the given figure, △BCD is a triangle in which BE is the internal bisector of ∠B and DF ∥ EB meeting CB produced at F . ∠BDF =
  • (i)
    ∠EDB
  • (ii)
    ∠FBD
  • (iii)
    ∠BED
  • (iv)
    ∠CEB
  • (v)
    ∠DFB
Question 24
24.
In the given figure, I and J are points on the sides FG and FH respectively of △FGH.For which of the following cases, IJ ∥ GH
a)
FI = 10 cm, IG = 8 cm, FJ = 10 cm and JH = 8 cm
b)
FG = 18 cm, IG = 8 cm, FJ = 12 cm and FH = 18 cm
c)
FG = 18 cm, FI = 12 cm, FH = 18 cm and JH = 8 cm
d)
FG = 18 cm, IG = 8 cm, FH = 18 cm and FJ = 10 cm
  • (i)
    {a,d}
  • (ii)
    {b,d,a}
  • (iii)
    {b,c,a}
  • (iv)
    {c,d}
  • (v)
    {b,a}
Question 25
25.
In the given figure, the area of the △KLM is x sq.cm. N,O,P are the mid-points of the sides LM , MK and KL respectively. The area of the △NOP is
  • (i)
      • 3

        4
      • of area of △KLM
  • (ii)
      • 1

        2
      • of area of △KLM
  • (iii)
      • 2

        3
      • of area of △KLM
  • (iv)
      • 1

        3
      • of area of △KLM
  • (v)
      • 1

        4
      • of area of △KLM
Question 26
26.
    • In the given figure, the parallelogram HIJK and the triangle △LHI are on the same bases and between the same parallels.
    • The area of the
    • △LHI
    • is x sq.cm. The area of the parallelogram is
  • (i)
      • 5

        4
      • the area of the triangle
  • (ii)
      • twice
      • the area of the triangle
  • (iii)
      • 3

        2
      • the area of the triangle
  • (iv)
      • thrice
      • the area of the triangle
  • (v)
      • 4

        3
      • the area of the triangle
Question 27
27.
If the ratio of the bases of two triangles is C : D and the ratio of the corresponding heights is E : F , the ratio of their areas in the same order is
  • (i)
    EF : CD
  • (ii)
    CD : EF
  • (iii)
    CF : DE
  • (iv)
    DE : CF
  • (v)
    CE : DF
Question 28
28.
In the given △GHI, JK ∥ HI. If  GJ : JH = 7.71 cm : 10.29 cm  and  GI = 18 cm, KI =
  • (i)
    12.29 cm
  • (ii)
    9.29 cm
  • (iii)
    11.29 cm
  • (iv)
    10.29 cm
  • (v)
    8.29 cm
Question 29
29.
In the given two similar triangles, if d = 19 cm, e = 18 cm, f = 20 cm, h = 10.8 cm, find i
  • (i)
    11.00 cm
  • (ii)
    12.00 cm
  • (iii)
    14.00 cm
  • (iv)
    10.00 cm
  • (v)
    13.00 cm
Question 30
30.
In the given figure, given ∠IFG = ∠HFI, x : y = 10.31 cm : 8.69 cm and p = 19 cm, find q =
  • (i)
    16.00 cm
  • (ii)
    18.00 cm
  • (iii)
    17.00 cm
  • (iv)
    15.00 cm
  • (v)
    14.00 cm
Question 31
31.
In the given figure, given ∠DAB = ∠CAD, p = 10.81 cm, q = 9.19 cm and BC = 20 cm, find BD =
  • (i)
    9.81 cm
  • (ii)
    8.81 cm
  • (iii)
    12.81 cm
  • (iv)
    10.81 cm
  • (v)
    11.81 cm
Question 32
32.
In the given figure, ABCD is a trapezium where OB = 13 cm , OC = 4 cm and OD = 4 cm . Find OA =
  • (i)
    12 cm
  • (ii)
    14 cm
  • (iii)
    11 cm
  • (iv)
    15 cm
  • (v)
    13 cm
Question 33
33.
In the given figure, ∠IFG = 51.52°, find the value of x =
  • (i)
    39.48°
  • (ii)
    36.48°
  • (iii)
    40.48°
  • (iv)
    38.48°
  • (v)
    37.48°
Question 34
34.
In the given figure, ∠GHI = 43.83°, find the value of y =
  • (i)
    46.17°
  • (ii)
    48.17°
  • (iii)
    45.17°
  • (iv)
    44.17°
  • (v)
    47.17°
Question 35
35.
In the given figure, if IJ ∥ KL then
  • (i)
    △IJM ∼ △LKM
  • (ii)
    △IJM ∼ △MLK
  • (iii)
    △MIJ ∼ △MKL
  • (iv)
    △MJI ∼ △MLK
  • (v)
    △IJM ∼ △MKL
Question 36
36.
In the given figure, △DEF is right-angled at E. Also, EG ⟂ DF. Which of the following are true?
a)
    • DE
      2
    • =
    • DF
    • .
    • DG
b)
    • EF
      2
    • =
    • FD
    • .
    • FG
c)
    • DE
      2
    • =
    • FD
    • .
    • FG
d)
    • EG
      2
    • =
    • DG
    • .
    • GF
e)
    • EF
      2
    • =
    • DF
    • .
    • DG
  • (i)
    {a,b,d}
  • (ii)
    {c,a,b}
  • (iii)
    {c,a}
  • (iv)
    {c,e,d}
  • (v)
    {e,b}
Question 37
37.
In the given figure, △GHI is right-angled at H. Also, HJ ⟂ GI. If  GH = 15 cm, HI = 18 cm, then find HJ.
  • (i)
    12.52 cm
  • (ii)
    11.52 cm
  • (iii)
    13.52 cm
  • (iv)
    10.52 cm
  • (v)
    9.52 cm
Question 38
38.
In the given figure, △BCD is right-angled at C. Also, CE ⟂ BD. If  BE = 13 cm, ED = 14.6 cm, then find CE.
  • (i)
    15.78 cm
  • (ii)
    13.78 cm
  • (iii)
    11.78 cm
  • (iv)
    12.78 cm
  • (v)
    14.78 cm
Question 39
39.
    • In the given figure, △DEF ∼ △MNO and DE = 13 cm, MN = 18.2 cm.
    • If the area of the
    • △MNO
    • =
    • 104.75 sq.cm
    • , find the area of the
    • △DEF
  • (i)
    53.44 sq.cm
  • (ii)
    55.44 sq.cm
  • (iii)
    52.44 sq.cm
  • (iv)
    54.44 sq.cm
  • (v)
    51.44 sq.cm
Question 40
40.
    • In the given figure, △ABC ∼ △OPQ and BC = 10 cm , PQ = 14 cm and
    • AD
    • =
    • 12.48 cm
    • ,
    • find the area of the
    • △OPQ
  • (i)
    121.28 sq.cm
  • (ii)
    122.28 sq.cm
  • (iii)
    123.28 sq.cm
  • (iv)
    120.28 sq.cm
  • (v)
    124.28 sq.cm
Question 41
41.
In the given figure, △EFG & △MNO are similar triangles. If the ratio of the heights EH : MP = 10 : 14, then the ratio of their areas is
  • (i)
    100
    sq.cm
    :
    193
    sq.cm
  • (ii)
    100
    sq.cm
    :
    198
    sq.cm
  • (iii)
    99
    sq.cm
    :
    196
    sq.cm
  • (iv)
    101
    sq.cm
    :
    196
    sq.cm
  • (v)
    100
    sq.cm
    :
    196
    sq.cm
Question 42
42.
In the given figure, points O , P and Q are the mid-points of sides MN, NL and LM of △LMN. Which of the following are true?
a)
Area of trapezium MNPQ is thrice the area of △LQP
b)
    • Area of trapezium
    • MNPQ
    • is
    • 1

      4
    • the area of
    • △LMN
c)
All four small triangles have equal areas
d)
Area of △LMN = 4 times area of △OPQ
e)
    • Area of
    • △LMN
    • =
    • 1

      3
    • area of
    • △OPQ
  • (i)
    {a,c,d}
  • (ii)
    {b,a,c}
  • (iii)
    {b,e,d}
  • (iv)
    {b,a}
  • (v)
    {e,c}
Question 43
43.
In the given figure, points G , H and I are the mid-points of sides EF, FD and DE of △DEF. Which of the following are true?
a)
△IEG ∼ △DEF
b)
△HGF ∼ △DEF
c)
△GHI ∼ △DEF
d)
△DIH ∼ △DEF
e)
△GIH ∼ △DEF
  • (i)
    {e,c}
  • (ii)
    {e,d,a}
  • (iii)
    {a,b,c,d}
  • (iv)
    {e,b}
  • (v)
    {e,a}
Question 44
44.
The perimeters of two similar triangles are 30 cm and 23 cm respectively. If one side of the first triangle is 16 cm, find the length of the corresponding side of the second triangle.
  • (i)
    14.27 cm
  • (ii)
    10.27 cm
  • (iii)
    12.27 cm
  • (iv)
    11.27 cm
  • (v)
    13.27 cm
Question 45
45.
In the given figure, D is a point on side BC of △ABC such that ∠CAB = ∠ADC = 100° , ∠DCA = 22°. Find ∠CAD
  • (i)
    57°
  • (ii)
    56°
  • (iii)
    60°
  • (iv)
    58°
  • (v)
    59°
Question 46
46.
HIJK is a square and △HIL is an equilateral triangle. Also, △HJM is an equilateral triangle. If area of △HIL is 'a' sq.units, then the area of △HJM is
  • (i)
      • a
        2
      • sq.units
  • (ii)
      • 1

        2



        3
      • a sq.units
  • (iii)



      • 3
      • a sq.units
  • (iv)
      • 1

        2
      • a sq.units
  • (v)
      • 2a sq.units
Question 47
47.
ABCD is a cyclic trapezium. Diagonals BD and AC intersect at E. If DA = 16 cm, find BC
  • (i)
    15 cm
  • (ii)
    18 cm
  • (iii)
    14 cm
  • (iv)
    16 cm
  • (v)
    17 cm
Question 48
48.
    • A vertical stick
    • 11 m
    • long casts a shadow of
    • 13 m
    • long on the ground.
    • At the same time, a tower casts the shadow
    • 104 m
    • long on the ground.
    • Find the height of the tower.
  • (i)
    88 m
  • (ii)
    90 m
  • (iii)
    87 m
  • (iv)
    86 m
  • (v)
    89 m
Question 49
49.
    • In the given figure, △GHI, PQ ∥ HI such that
    • area of
    •  
    • △GPQ
    • = area of
    •  
    • PQIH
    • . Find
    •  
    • GP

      GH
  • (i)
    1

    2



    2
  • (ii)
    1

    2



    4
  • (iii)
    1

    2



    1

    2
  • (iv)
    1

    2
    4


    2
  • (v)
    1
Question 50
50.
In the given figure, ∠FCD = ∠ECF and CF ∥ GE and CD = 20 cm, DF = 10 cm and FE = 9 cm. Find CG
  • (i)
    20.00 cm
  • (ii)
    17.00 cm
  • (iii)
    18.00 cm
  • (iv)
    19.00 cm
  • (v)
    16.00 cm
Question 51
51.
    • In the given figure, IK is the angular bisector of
    • ∠I
    • &
    • ∠K
    • HI
    • =
    • 20 cm
    • ,
    • IJ
    • =
    • 21 cm
    • and
    • JK
    • =
    • 26 cm
    • .
    • Find
    • KH
  • (i)
    22.76 cm
  • (ii)
    23.76 cm
  • (iii)
    25.76 cm
  • (iv)
    26.76 cm
  • (v)
    24.76 cm
Question 52
52.
In the given figure, CDE is a triangle and 'O' is a point inside △CDE. The angular bisector of ∠DOC, ∠EOD & ∠COE meet CD, DE & EC at F, G & H respectively . Then
  • (i)
    CF . DG . EH = OC . OD . OE
  • (ii)
    CF . DG . EH = CD . DE . EC
  • (iii)
    CF . DG . EH = FG . GH . HF
  • (iv)
    CF . DG . EH = FD . GE . HC
  • (v)
    CF . DG . EH = OF . OG . OH
Question 53
53.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 24 cm and AP = 10 cm. Find PB
  • (i)
    12.00 cm
  • (ii)
    16.00 cm
  • (iii)
    14.00 cm
  • (iv)
    13.00 cm
  • (v)
    15.00 cm
Question 54
54.
From the given figure and values, find x
  • (i)
    (
    33
    ,
    -1
    )
  • (ii)
    (
    1
    ,
    35
    )
  • (iii)
    (
    34
    ,
    0
    )
  • (iv)
    (
    35
    ,
    -1
    )
  • (v)
    (
    33
    ,
    -2
    )
Question 55
55.
If the measures are as shown in the given figure, find  HI
  • (i)
    22.0 cm
  • (ii)
    21.0 cm
  • (iii)
    25.0 cm
  • (iv)
    24.0 cm
  • (v)
    23.0 cm
Question 56
56.
    • In the given figure, the two circles touch each other internally.
    • Diameter
    • OB
    • passes through the centre of the smaller circle.
    • OX = 9 cm
    • ,
    • OY = 20 cm
    • and radius of the inner circle is
    • 5.5 cm
    • .
    • Find the radius of the outer circle.
  • (i)
    11.22 cm
  • (ii)
    13.22 cm
  • (iii)
    10.22 cm
  • (iv)
    14.22 cm
  • (v)
    12.22 cm
    Assignment Key

  •  1) (i)
  •  2) (iii)
  •  3) (iv)
  •  4) (i)
  •  5) (ii)
  •  6) (ii)
  •  7) (iii)
  •  8) (ii)
  •  9) (iii)
  •  10) (ii)
  •  11) (iii)
  •  12) (iii)
  •  13) (ii)
  •  14) (iii)
  •  15) (i)
  •  16) (v)
  •  17) (ii)
  •  18) (iv)
  •  19) (iii)
  •  20) (v)
  •  21) (ii)
  •  22) (i)
  •  23) (v)
  •  24) (i)
  •  25) (v)
  •  26) (ii)
  •  27) (v)
  •  28) (iv)
  •  29) (ii)
  •  30) (i)
  •  31) (iv)
  •  32) (v)
  •  33) (iv)
  •  34) (i)
  •  35) (i)
  •  36) (i)
  •  37) (ii)
  •  38) (ii)
  •  39) (i)
  •  40) (ii)
  •  41) (v)
  •  42) (i)
  •  43) (iii)
  •  44) (iii)
  •  45) (iv)
  •  46) (v)
  •  47) (iv)
  •  48) (i)
  •  49) (i)
  •  50) (iii)
  •  51) (v)
  •  52) (iv)
  •  53) (iii)
  •  54) (i)
  •  55) (v)
  •  56) (v)