IN triangle ABC points M and N on side AB and AC respectively are taken, so that AM=1/4 AB and AN=1/4AC.Prove that MN =1/4BC.

i apologise for not providing the fig.

in triangle ABC

let P be the mid point of AB and Q be the id point of AC.

{by mid point th}

PQ//BC and PQ=1/2BC {2PQ=BC} - EQ 1

in triangle APQ

M is the mid point of AP and N is the mid point of AQ.

{by mid point th]

MN//PQ, MN=1/2PQ{2MN=PQ] -EQ 2

substitute EQ2 in EQ 1

2{2MN}=BC

4 MN= BC

MN=1/4 BC