Question

g) In the given triangle ABC, two medians BE and CD are
intersecting at 0. Prove that
area of ABOC = area of quad. ADOE
​

Answer 1

answer

BE is the median of ΔABC

so, ar(ΔBEC)=

2

1

ar(ΔABC) __(1)

Median of triangle divides into 2 triangles of equal area.

Also CF is median of ΔABC

⇒ar(ΔACF)=

2

1

ar(ΔABC) __(2)

from (1) and (2)

ar(ΔACF)=ar(ΔBEC)

ar(ΔGBC)+ar(ΔGEC)=ar(AFGE)+ar(GEC)

∴ar(ΔGBC)=ar(AFGE)