ICSE Board Practice

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ICSE Grade IX - Mid-Point and Intercept Theorems
Question 1
1.
ABCD is a quadrilateral. P, Q, R and S are mid-points of AB, BC, CD and DA respectively.If  AC = 29 cm and BD = 15 cm, find the measure of the sides of PQRS.
      • 15 cm
      • ,
      • 7.5 cm
      • ,
      • 15 cm
      • ,
      • 7.5 cm
      • 14.5 cm
      • ,
      • 7.5 cm
      • ,
      • 14.5 cm
      • ,
      • 7.5 cm
      • 14.5 cm
      • ,
      • 6 cm
      • ,
      • 14.5 cm
      • ,
      • 6 cm
      • 14.5 cm
      • ,
      • 5 cm
      • ,
      • 14.5 cm
      • ,
      • 5 cm
      • 17 cm
      • ,
      • 7.5 cm
      • ,
      • 17 cm
      • ,
      • 7.5 cm
Question 2
2.
In the given figure, points I , J and K are the mid-points of sides GH, HF and FG of △FGH. Which of the following are true?
a)
    • Area of
    • △FGH
    • =
    • 1
      3
    • area of
    • △IJK
b)
    • Area of trapezium
    • GHJK
    • is
    • 1
      4
    • the area of
    • △FGH
c)
Area of △FGH = 4 times area of △IJK
d)
All four small triangles have equal areas
e)
Area of trapezium GHJK is thrice the area of △FKJ
  • {a,c,d}
  • {a,b,e}
  • {a,c}
  • {b,d}
  • {c,d,e}
Question 3
3.
In the given figure, HIJK is a trapezium. L and M are mid-points of HK and IJ.Given JK = 7 cm and HI = 18 cm, find LM
  • 11.5 cm
  • 12.5 cm
  • 13.5 cm
  • 14.5 cm
  • 10.5 cm
Question 4
4.
    • In the given figure
    • △KLM
    • ,
    • N
    • is the mid-point of
    •  
    •  

      KL
       
       
    • and
    •  
    •  

      NO
       
       
      ∥
       

      LM
       
       
    • ,
    • then
    •  
    • OM
    • =
  • MK
  • KO
  • KN
  • KL
  • NL
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.
    • ∠AFD  =
  • ∠HAB
  • ∠FEH
  • ∠FDA
  • ∠FAC
  • ∠HFE
Question 6
6.
    • 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.
    • △ABH ∼
  • △ACF
  • △FDA
  • △FEH
  • △DAE
  • △DCF
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.
    • ∠CFA  =
  • ∠EHF
  • ∠DAF
  • ∠HFE
  • ∠BHA
  • ∠AFD
Question 8
8.
From the given figure and values, find x
  • (
    1
    ,
    15
    )
  • (
    15
    ,
    -1
    )
  • (
    13
    ,
    -1
    )
  • (
    14
    ,
    0
    )
  • (
    13
    ,
    -2
    )
Question 9
9.
In the given figure, the area of the △FGH is x sq.cm. I,J,K are the mid-points of the sides GH , HF and FG respectively. The area of the △IJK is
      • 2
        3
      • of area of △FGH
      • 3
        4
      • of area of △FGH
      • 1
        4
      • of area of △FGH
      • 1
        3
      • of area of △FGH
      • 1
        2
      • of area of △FGH
Question 10
10.
    • In the given figure, GHIJ is a parallelogram
    • such that
    • K
    • and
    • L
    • are mid-points of sides
    • GH
    • &
    • IJ
    • .
    • GL
    • meets
    • HJ
    • at
    • S
    • and
    • IK
    • meets
    • HJ
    • at
    • T
    • . Given
    • HJ
    • =
    • 16 cm
    • , find
    • SJ
  • 3.33 cm
  • 4.33 cm
  • 6.33 cm
  • 7.33 cm
  • 5.33 cm