Please prove?

In the figure below ABCE is a paralleogram. F and G are an points on CE and EB respectively such that FG is parallel to CB. Prove that area of #DeltaACF=DeltaABG# enter image source here

1 Answer
May 21, 2018

see explanation.

Explanation:

enter image source here
let #|ABC|# denote area of #ABC#,
let #BG=w, GE=x, CF=y, FE=z#,
given #FG# // #CB#,
#=> w/(w+x)=y/(y+z)#
#|ABG|/|ABE|=w/(w+x)#
#|ACF|/|ACE|=y/(y+z)#
As #|ABE|=|ACE|=1/2*|ABEC|#
#=> |ABG|:|ACF|=w/(w+x):y/(y+z)=1:1#
#=> |ACF|=|ABG|#