Given : A triangle ABC in which D and E are mid point of sides AB and AC respectively.
To Prove : DE || BC
Proof : Since sides AB and AC have D and E as mid points,
\(\therefore\) AD = DB and AE = EC
\(\implies\) \(AD\over DB\) = 1 and \(AE\over EC\) = 1
\(\implies\) \(AD\over DB\) = \(AE\over EC\)
Hence, By converse of Basic proportionality theorem,
DE || BC.