Question
P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(ΔAPB) = ar{ΔBQC).
Solution
Given: P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD.
To Prove: ar(ΔAPB) = ar(ΔBQC).
Proof: ∵ ΔAPB and || gm ABCD are on the same base AB and between the same parallels AB and DC.
∵ ΔBQC and || gm ABCD are on the same base BC and between the same parallels BC and AD.
From (1) and (2),
ar(ΔAPB) = ar(ΔBQC).
To Prove: ar(ΔAPB) = ar(ΔBQC).
Proof: ∵ ΔAPB and || gm ABCD are on the same base AB and between the same parallels AB and DC.
∵ ΔBQC and || gm ABCD are on the same base BC and between the same parallels BC and AD.
From (1) and (2),
ar(ΔAPB) = ar(ΔBQC).
