If ABCD is a parallelogram, then prove that

Given:-

ABCD is a parallelogram,

To prove: - Ar (ΔABD) = Ar(ΔBCD) = Ar(ΔABC) = Ar(ΔACD) = (1/2) Ar (//^gm ABCD).

Proof:- We know that diagonal of a parallelogram divides it into two equilaterals .

Since, AC is the diagonal.

Then, Ar (ΔABC) = Ar(ΔACD) = (1/2) Ar(// ^gm ABCD)   ⋅⋅⋅⋅ (1)

Since, BD is the diagonal.

Then,  Ar(ΔABD) = Ar(ΔBCD) = (1/2) Ar(// ^gm ABCD)   ⋅⋅⋅⋅⋅ (2)

Compare equation (1) and (2)

∴  Ar(ΔABC) = Ar(ΔACD) = Ar(ΔABD) = Ar(ΔBCD) = (1/2) Ar(// ^gm ABCD)..