ICSE Board Practice

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ICSE Grade IX - Mid-Point and Intercept Theorems
Question 1
1.
In the given figure, points P , Q and R are the mid-points of sides NO, OM and MN of △MNO. Which of the following are true?
a)
Area of △MNO = 4 times area of △PQR
b)
Area of trapezium NOQR is thrice the area of △MRQ
c)
    • Area of trapezium
    • NOQR
    • is
    • 1
      4
    • the area of
    • △MNO
d)
All four small triangles have equal areas
e)
    • Area of
    • △MNO
    • =
    • 1
      3
    • area of
    • △PQR
  • {e,b}
  • {c,a}
  • {a,b,d}
  • {c,e,d}
  • {c,a,b}
Question 2
2.
    • In the given figure
    • △BCD
    • ,
    • E
    • is the mid-point of
    •  
    •  

      BC
       
       
    • and
    •  
    •  

      EF
       
       
      ∥
       

      CD
       
       
    • ,
    • then
    •  
    • FD
    • =
  • BE
  • BC
  • DB
  • EC
  • BF
Question 3
3.
In the given figure, IJKL is a parallelogram such that Q is the mid-point of IJ and  IJ = 2LI. Find ∠LQK
  • 91°
  • 90°
  • 92°
  • 88°
  • 89°
Question 4
4.
In the given figure, if A, Q, R, S, T, U are equidistant and RP ∥ UB and AB = 20 cm and AP = 8 cm. Find PB
  • 12.00 cm
  • 14.00 cm
  • 13.00 cm
  • 11.00 cm
  • 10.00 cm
Question 5
5.
BCDE is a quadrilateral. R, S, T and U are mid-points of BC, CD, DE and EB respectively.If  BD = 28 cm and CE = 17 cm, find the measure of the sides of RSTU.
      • 14 cm
      • ,
      • 7 cm
      • ,
      • 14 cm
      • ,
      • 7 cm
      • 15 cm
      • ,
      • 8.5 cm
      • ,
      • 15 cm
      • ,
      • 8.5 cm
      • 14 cm
      • ,
      • 8.5 cm
      • ,
      • 14 cm
      • ,
      • 8.5 cm
      • 14 cm
      • ,
      • 5 cm
      • ,
      • 14 cm
      • ,
      • 5 cm
      • 16 cm
      • ,
      • 8.5 cm
      • ,
      • 16 cm
      • ,
      • 8.5 cm
Question 6
6.
    • In the given figure, △BCD is a triangle.
    • E
    • ,
    • F
    • &
    • G
    • are mid-points of
    • CD
    • ,
    • DB
    • &
    • BC
    • respectively.
    • Given
    • EF = 9 cm
    • ,
    • FG = 9 cm
    • &
    • GE = 9 cm
    • ,
    • find the sides of the triangle.
      • 19 cm
      • ,
      • 18 cm
      • &
      • 18 cm
      • 18 cm
      • ,
      • 18 cm
      • &
      • 18 cm
      • 18 cm
      • ,
      • 18 cm
      • &
      • 21 cm
      • 18 cm
      • ,
      • 17 cm
      • &
      • 18 cm
      • 16 cm
      • ,
      • 18 cm
      • &
      • 18 cm
Question 7
7.
    • In the given figure
    • △FGH
    • ,
    • I
    • is the mid-point of
    •  
    •  

      FG
       
       
    • and
    •  
    •  

      IJ
       
       
      ∥
       

      GH
       
       
    • ,
    • then
    •  
    • IG
    • =
  • FG
  • FI
  • FJ
  • HF
  • JH
Question 8
8.
    • In the given figure, DEFG is a parallelogram
    • such that
    • H
    • and
    • I
    • are mid-points of sides
    • DE
    • &
    • FG
    • .
    • DI
    • meets
    • EG
    • at
    • T
    • and
    • FH
    • meets
    • EG
    • at
    • U
    • . Given
    • EG
    • =
    • 17 cm
    • , find
    • TU
  • 3.67 cm
  • 7.67 cm
  • 5.67 cm
  • 6.67 cm
  • 4.67 cm
Question 9
9.
    • In the given figure
    • △JKL
    • ,
    • M
    • is the mid-point of
    •  
    •  

      JK
       
       
    • and
    •  
    •  

      MN
       
       
      ∥
       

      KL
       
       
    • ,
    • then
    •  
    • JN
    • =
  • LJ
    2
  • KL
    2
  • JK
    2
  • KL
  • JM
Question 10
10.
    • 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  =
  • ∠DAF
  • ∠ACF
  • ∠ABH
  • ∠FEH
  • ∠EHF