ICSE Board Practice

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ICSE Grade IX - Mid-Point and Intercept Theorems

Question 1

1.	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. △ACF ∼
	△DCF △DAE △FEH △FDA △ABH

Question 2

2.	In the given figure △ABC , D is the mid-point of     AB     and     DE     ∥   BC     , then   EC =
	AE AD DB AB CA

Question 3

3.	In the given figure △KLM , N is the mid-point of     KL     and     NO     ∥   LM     , then   KO =
	LM 2 KL 2 KN MK 2 LM

Question 4

4.	In the given figure, the area of the △GHI is x sq.cm. J,K,L are the mid-points of the sides HI , IG and GH respectively. The area of the △JKL is
	3 4 of area of △GHI 1 3 of area of △GHI 1 2 of area of △GHI 2 3 of area of △GHI 1 4 of area of △GHI

Question 5

5.	In the given figure △KLM , N is the mid-point of     KL     and     NO     ∥   LM     , then   NL =
	OM KL KO KN MK

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. ∠DAF  =
	∠BHA ∠AFD ∠EHF ∠CFA ∠HFE

Question 7

7.	In the given figure, △CDE is a triangle. F , G & H are mid-points of DE , EC & CD respectively. Given FG = 9 cm , GH = 9 cm & HF = 9 cm , find the sides of the triangle.
	18 cm , 18 cm & 18 cm 15 cm , 18 cm & 18 cm 18 cm , 17 cm & 18 cm 19 cm , 18 cm & 18 cm 18 cm , 18 cm & 20 cm

Question 8

8.	In the given figure △CDE , F is the mid-point of     CD     and     FG     ∥   DE     , then   CG =
	FD CD CF EC GE

Question 9

9.	In the given figure △CDE , F is the mid-point of     CD     and     FG     ∥   DE     , then   CF =
	EC 2 CD 2 CG DE 2 DE

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. ∠FEH  =
	∠ABH ∠DAF ∠ACF ∠FDA ∠EHF

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