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Question

$$D$$ and $$E$$ are points on the sides $$AB$$ and $$AC$$ respectively of a $$\triangle ABC$$. In each of the following cases, determine whether $$DE || BC$$ or not. $$AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm$$ and $$EC = 8 cm$$ 
1713749_563852f451b04433921f100fff77cd0a.png


Solution

From figure, $$D$$ and $$E$$ are the points on the sides $$AB$$ and $$AC$$ of $$\triangle ABC$$  
 
$$AD = 5.7 cm, \ DB = 9.5 cm, \ AE = 4.8 cm$$ and $$EC = 8 cm$$ 
 
$$\dfrac{AD}{DB} =  \dfrac{5.7}{9.5} = \dfrac{3}{5}$$ 
 
and $$\dfrac{AE}{EC} = \dfrac{4.8}{8} = \dfrac{3}{5}$$ 
 
$$\Rightarrow \dfrac{AD}{DB} = \dfrac{AE}{EC}$$ 

$$\therefore $$ by converse of basic proportionality theorem
 
$$\Rightarrow DE || BC$$ 

Mathematics
RS Agarwal
Standard X

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