ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade IX - Similarity
Question 1
1.
    • In the given figure, △ABC and △RST are such that
    • AB
      RS
    • =
    • BC
      ST
    • =
    • CA
      TR
    • .
    • Identify the property by which the two triangles are similar
  • AAA Similarity
  • SAS Similarity
  • not similar
  • SSS Similarity
Question 2
2.
In the given figure, BCD is a triangle and 'O' is a point inside △BCD. The angular bisector of ∠COB, ∠DOC & ∠BOD meet BC, CD & DB at E, F & G respectively . Then
  • BE . CF . DG = OE . OF . OG
  • BE . CF . DG = OB . OC . OD
  • BE . CF . DG = EC . FD . GB
  • BE . CF . DG = BC . CD . DB
  • BE . CF . DG = EF . FG . GE
Question 3
3.
    • 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  =
  • ∠HFE
  • ∠FDA
  • ∠HAB
  • ∠FAC
  • ∠FEH
Question 4
4.
Which of the following are necessary conditions for similarity of two polygons ?
a)
The corresponding sides are equal.
b)
The corresponding sides are proportional.
c)
The corresponding angles are equal.
d)
The corresponding angles are proportional.
  • {a,d,b}
  • {a,b}
  • {b,c}
  • {a,c,b}
  • {d,c}
Question 5
5.
In the given figure, △ABC is right-angled at B. Also, BD ⟂ AC. If  AB = 19 cm, BC = 17 cm, then find BD.
  • 11.67 cm
  • 12.67 cm
  • 13.67 cm
  • 14.67 cm
  • 10.67 cm
Question 6
6.
In the given figure, ∠EFG = 36.87°, find the value of y =
  • 55.13°
  • 52.13°
  • 53.13°
  • 51.13°
  • 54.13°
Question 7
7.
    • The ratio of the bases of two triangles ABC and DEF is
    • 10
      		:
      3
    • .
    • If the triangles are equal in area, then the ratio of their heights is
  • 10
    		:
    1
  • 9
    		:
    3
  • 11
    		:
    3
  • 10
    		:
    6
  • 3
    		:
    10
Question 8
8.
Which of the following are true?
a)
Area of the union of two polygonal region is the sum of the individual area.
b)
Area of a convex polygonal region is equal to the sum of the areas of all triangles formed by joining the vertices of the polygon with an interior point.
c)
Area of the union of two polygonal region is not equal to the sum of the individual area.
d)
A polygonal region can be divided into a finite number of triangles in a unique way.
  • {d,c}
  • {a,c,b}
  • {b,c}
  • {a,b}
  • {a,d,b}
Question 9
9.
In the given figure, points J , K and L are the mid-points of sides HI, IG and GH of △GHI. Which of the following are true?
a)
△JKL ∼ △GHI
b)
△LHJ ∼ △GHI
c)
△JLK ∼ △GHI
d)
△KJI ∼ △GHI
e)
△GLK ∼ △GHI
  • {c,a}
  • {c,d}
  • {a,b,d,e}
  • {c,e,a}
  • {c,b}
Question 10
10.
In an equilateral triangle ABC, the side BC is trisected at D. Then
      • 9 AD
        2
      • =
      • 7 AB
        2
      • 7 AD
        2
      • =
      • 9 AB
        2
      • 7 AD
        2
      • =
      • 3 AB
        2
      • 3 AD
        2
      • =
      • 7 AB
        2