Question

In parallelogram ABCD, E and F are any two points on the side AB and BC respectively. Show that ar( △ADF)=ar( △DCE) (hint- draw EG| |AD, FH| |AB)

Answer 1

Ans. In ABC, points D and E divides BC in three equal parts such that BD = DE = EC.

BD = DE = EC =  BC

Draw AFBC

ar (ABC) =  ……….(i)

and ar (ABD) = ……….(ii)

=  = 

=  ar (ABC) ……….(iii)

And ar (AEC) =  ar (ABC) ……….(iv)

From (ii), (iii) and (iv),

ar (ABD) = ar (ADE) = ar (AEC)
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