ICSE Board Practice

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ICSE Grade IX - Mid-Point and Intercept Theorems
Question 1
1.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 21 cm and AP = 8 cm. Find PB
  • 13.00 cm
  • 14.00 cm
  • 12.00 cm
  • 15.00 cm
  • 11.00 cm
Question 2
2.
ABCD is a quadrilateral. T, U, V and W are mid-points of AB, BC, CD and DA respectively.If  AC = 29 cm and BD = 17 cm, find the measure of the sides of TUVW.
      • 14.5 cm
      • ,
      • 8.5 cm
      • ,
      • 14.5 cm
      • ,
      • 8.5 cm
      • 14.5 cm
      • ,
      • 5 cm
      • ,
      • 14.5 cm
      • ,
      • 5 cm
      • 14.5 cm
      • ,
      • 7 cm
      • ,
      • 14.5 cm
      • ,
      • 7 cm
      • 17 cm
      • ,
      • 8.5 cm
      • ,
      • 17 cm
      • ,
      • 8.5 cm
      • 15 cm
      • ,
      • 8.5 cm
      • ,
      • 15 cm
      • ,
      • 8.5 cm
Question 3
3.
In the given figure, the area of the △MNO is x sq.cm. P,Q,R are the mid-points of the sides NO , OM and MN respectively. The area of the △PQR is
      • 1
        3
      • of area of △MNO
      • 3
        4
      • of area of △MNO
      • 1
        4
      • of area of △MNO
      • 2
        3
      • of area of △MNO
      • 1
        2
      • of area of △MNO
Question 4
4.
    • In the given figure, CDEF is a parallelogram
    • such that
    • G
    • and
    • H
    • are mid-points of sides
    • CD
    • &
    • EF
    • .
    • CH
    • meets
    • DF
    • at
    • Q
    • and
    • EG
    • meets
    • DF
    • at
    • R
    • . Given
    • DF
    • =
    • 16 cm
    • , find
    • QF
  • 4.33 cm
  • 3.33 cm
  • 5.33 cm
  • 7.33 cm
  • 6.33 cm
Question 5
5.
    • In the given figure, △JKL is a triangle.
    • M
    • ,
    • N
    • &
    • O
    • are mid-points of
    • KL
    • ,
    • LJ
    • &
    • JK
    • respectively.
    • Given
    • MN = 9 cm
    • ,
    • NO = 10 cm
    • &
    • OM = 8 cm
    • ,
    • find the sides of the triangle.
      • 18 cm
      • ,
      • 19 cm
      • &
      • 16 cm
      • 19 cm
      • ,
      • 20 cm
      • &
      • 16 cm
      • 16 cm
      • ,
      • 20 cm
      • &
      • 16 cm
      • 18 cm
      • ,
      • 20 cm
      • &
      • 16 cm
      • 18 cm
      • ,
      • 20 cm
      • &
      • 18 cm
Question 6
6.
    • In the given figure
    • △KLM
    • ,
    • N
    • is the mid-point of
    •  
    •  

      KL
       
       
    • and
    •  
    •  

      NO
       
       
      ∥
       

      LM
       
       
    • ,
    • then
    •  
    • NL
    • =
  • KN
  • KO
  • MK
  • OM
  • KL
Question 7
7.
    • In the given figure
    • △IJK
    • ,
    • L
    • is the mid-point of
    •  
    •  

      IJ
       
       
    • and
    •  
    •  

      LM
       
       
      ∥
       

      JK
       
       
    • ,
    • then
    •  
    • IL
    • =
  • JK
  • KI
    2
  • IJ
    2
  • JK
    2
  • IM
Question 8
8.
From the given figure and values, find x
  • (
    1
    ,
    11
    )
  • (
    -1
    ,
    10
    )
  • (
    0
    ,
    12
    )
  • (
    -1
    ,
    11
    )
  • (
    13
    ,
    1
    )
Question 9
9.
    • In the given figure
    • △BCD
    • ,
    • E
    • is the mid-point of
    •  
    •  

      BC
       
       
    • and
    •  
    •  

      EF
       
       
      ∥
       

      CD
       
       
    • ,
    • then
    •  
    • BF
    • =
  • DB
    2
  • CD
  • BC
    2
  • BE
  • CD
    2
Question 10
10.
In the given figure, points K , L and M are the mid-points of sides IJ, JH and HI of △HIJ. Which of the following are true?
a)
    • Area of
    • △HIJ
    • =
    • 1
      3
    • area of
    • △KLM
b)
Area of trapezium IJLM is thrice the area of △HML
c)
All four small triangles have equal areas
d)
Area of △HIJ = 4 times area of △KLM
e)
    • Area of trapezium
    • IJLM
    • is
    • 1
      4
    • the area of
    • △HIJ
  • {a,b,c}
  • {b,c,d}
  • {a,b}
  • {e,c}
  • {a,e,d}