ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Similarity of Triangles
Question 1
1.
In the given figure, CDEF is a trapezium where OC = 12 cm , OD = 12 cm and OE = 4 cm . Find OF =
  • 4 cm
  • 5 cm
  • 2 cm
  • 3 cm
  • 6 cm
Question 2
2.
    • In the given figure, FGHI is a trapezium in which
    • FG ∥ HI
    • and the diagonals
    • GI
    • and
    • FH
    • intersect at
    • J
    • .
    • If
    •  
    • JF
    • =
    • (
      5
      x
      +
      16
      		)
    • cm,
    • GJ
    • =
    • (
      4
      x
      +
      10
      		)
    • cm,
    • JH
    • =
    • (
      x
      +
      14
      		)
    • cm and
    • IJ
    • =
    • (
      x
      +
      6
      		)
    • cm, find the value of x
  • (
    22
    ,
    -2
    )
  • (
    24
    ,
    -2
    )
  • (
    23
    ,
    -1
    )
  • (
    0
    ,
    24
    )
  • (
    22
    ,
    -3
    )
Question 3
3.
GHIJ is a cyclic trapezium. Diagonals HJ and GI intersect at K. If JG = 15 cm, find HI
  • 15 cm
  • 17 cm
  • 16 cm
  • 14 cm
  • 13 cm
Question 4
4.
In the given figure, points F , G and H are the mid-points of sides DE, EC and CD of △CDE. Which of the following are true?
a)
All four small triangles have equal areas
b)
    • Area of trapezium
    • DEGH
    • is
    • 1
      4
    • the area of
    • △CDE
c)
    • Area of
    • △CDE
    • =
    • 1
      3
    • area of
    • △FGH
d)
Area of △CDE = 4 times area of △FGH
e)
Area of trapezium DEGH is thrice the area of △CHG
  • {b,a,d}
  • {c,d}
  • {a,d,e}
  • {b,a}
  • {b,c,e}
Question 5
5.
    • 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.
    • △FEH ∼
  • △DAE
  • △ACF
  • △DCF
  • △ABH
  • △FDA
Question 6
6.
    • In the given figure, △IJK and △PQR are such that
    • IJ
      PQ
    • =
    • JK
      QR
    • =
    • KI
      RP
    • .
    • Identify the property by which the two triangles are similar
  • SAS Similarity
  • SSS Similarity
  • not similar
  • AAA Similarity
Question 7
7.
    • 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.
    • ∠BHA  =
  • ∠EHF
  • ∠AFD
  • ∠DAF
  • ∠HFE
  • ∠CFA
Question 8
8.
In the given figure, ∠GEF = 41.38°, find the value of y =
  • 47.62°
  • 46.62°
  • 50.62°
  • 48.62°
  • 49.62°
Question 9
9.
In the given figure, H is a point on side FG of △EFG such that ∠GEF = ∠EHG = 101° , ∠HGE = 25°. Find ∠GEH
  • 53°
  • 55°
  • 54°
  • 56°
  • 52°
Question 10
10.
In the given figure, △HIJ is right-angled at I. Also, IK ⟂ HJ. If  KJ = 15.2 cm, IK = 12.99 cm, then find HK.
  • 11.10 cm
  • 10.10 cm
  • 12.10 cm
  • 9.10 cm
  • 13.10 cm