Question

In a ∆ABC, D,E,F are midpoints of BC, CA, AB. Show that BDEF is a llgm and ar(∆DEF)=1/4ar(∆ABC)

Answer 1

in tri. AND given that E, F and D are the midpoint
hence FE Is parallel to BC, DE parallel to AB and DF parallel to AC
by mid point theorem
if DR is parallel to B.S.
then DR is parallel to BF and FE Is parallel to BC
then FE Is parallel to be
therefore FEDB is a parallelogram in which DF is a digital and we know digital of parallelogram divides it into 2 tri. with equal areas

hence ar. of tri.BDF = ar.of tri.DEF 1
ar. of tri. CDR= ar. of tri.DEF 2
ar. of tri. AFE= ar. of tri. DEF 3
ar. of tri.DEF= ar. of tri.DEF 4

on adding 1 2 3 4
at. of tri.ABC= 4 ar. of tri. DEF
ar of tri. DEF= 1/4 ar. of tri. ABC