Question:
If ABCD is a parallelogram, then prove that
Ar (ΔABD) = Ar(ΔBCD) = Ar(ΔABC) = Ar(ΔACD) = (1/2) Ar (// gm ABCD).
Solution:
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)..