Q. 43.8( 17 Votes )

If ABCD is a parallelogram, then prove that

ar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC)=ar(Δ ACD) = ar(||gm ABCD)

Answer :

We know that,

Diagonal of parallelogram divides it into two quadrilaterals.


Since,


AC is the diagonal


Then, Area (ΔABC) = Area (ΔACD)


= Area of parallelogram ABCD (i)


Since,


BD is the diagonal


Then, Area (ΔABD) = Area (ΔBCD)


= Area of parallelogram ABCD (ii)


Compare (i) and (ii), we get


Therefore,


Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = Area of parallelogram ABCD


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