# If ABCD is a parallelogram, then prove thatar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC)=ar(Δ ACD) = ar(||gm ABCD)

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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