Question

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ΔABC. Show that

(i) BDEF is a parallelogram.

(ii) ar (DEF) = ar (ABC)

(iii) ar (BDEF) = ar (ABC)
Answer :

Answer 1

since D and E are mid point... then by mid point theorem
DE ll AB
DE || 1/2AB

similarly do it for EF and BD
then BDEF is parallelogram

similarly, DFEC , DFAE are also parallelogram
so ar(DEF) = ar(ABC)
and also ar(BDEF) = ar(ABC)