$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of a $△ A B C$ . In each of the following cases, determine whether $D E | | B C$ or not. $A D = 5.7 c m, D B = 9.5 c m, A E = 4.8 c m$ and $E C = 8 c m$

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Solution

From figure, $D$ and $E$ are the points on the sides $A B$ and $A C$ of $△ A B C$
$A D = 5.7 c m, D B = 9.5 c m, A E = 4.8 c m$ and $E C = 8 c m$
$\frac{A D}{D B} = \frac{5.7}{9.5} = \frac{3}{5}$
and $\frac{A E}{E C} = \frac{4.8}{8} = \frac{3}{5}$
$\Rightarrow \frac{A D}{D B} = \frac{A E}{E C}$

$∴$ by converse of basic proportionality theorem
$\Rightarrow D E | | B C$

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