Given,
Let P and Q be the mid points of AB and AC respectively
Then,
PQ || BC and
PQ = \(\frac{1}{2}\) BC ....(i)
In ∆APQ,
D and E are mid points of AP and AQ resp.
∴ DE || PQ ,
DE = \(\frac{1}{2}\)PQ ...(ii)
From (i) and (ii),
DE = \(\frac{1}{2}\)PQ = \(\frac{1}{2}\)(\(\frac{1}{2}\) BC)
DE = \(\frac{1}{4}\) BC Proved.