Question

If D, E are the points on the side AB and AC of triangle abc such that AD=6cm, BD=9cm, AE=8cm, EC=12cm. Prove that DE parallel to BC

Answer 1

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Answer 2

let us try basic proportionality theorem 

$\frac{AD}{DB} = \frac{AE}{EC}$


$\frac{6}{9} = \frac{8}{12}$

$\frac{2}{3}= \frac{2}{3}$

since it obeys basic proportionality theorem the line DE is parallel to BC