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Answer :
Given, in \(\triangle ABC\), D and E are the mid points of AB and AC respectively, such that,
AD=BD and AE=EC.
We have to prove that: DE || BC.
Since, D is the midpoint of AB
AD=DB
=>\(\frac{AD}{BD}\) = 1……………………………….. (i)
Also given, E is the mid-point of AC.
AE=EC
=> \(\frac{AE}{EC}\) = 1
From equation (i) and (ii), we get,
\(\frac{AD}{BD} = \frac{AE}{EC}\)
By converse of Basic Proportionality Theorem,
DE || BC
Hence, proved.