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In a triangle ABC ,D and E are points on the sides AB and AC respectively,such that BD=EC.prove that DE//BC

Posted by Parnish Sharma 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

In {tex}\triangle ABC{/tex} ,
{tex}\frac{AD}{DB}=\frac{6}{9}=\frac{2}{3}{/tex} ........... (i)

and {tex}\frac{AE}{EC}=\frac{8}{12}=\frac{2}{3}{/tex} ........... (ii)
From (i) and (ii)
{tex}\frac{AD}{DB}=\frac{AE}{EC}{/tex}
Hence, {tex}DE\parallel BC{/tex} [ By converse of basic proportionality theorem, if a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side. ]
Hence Proved.

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