Question

if ABCD is a parallelogram,then prove that ar(ABD)=ar( BCD)=ar(ABC)=ar(ACD)=1/2ar(parallelogram ABCD)​

Answer 1

Answer:

Step-by-step explanation:

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