Question
In figure, ABCD, DCFE and ABFE are parallelograms. Show that ar(ΔADE) = ar(ΔBCF).
Solution
Given: ABCD, DCFE and ABFE are parallelograms.
To Prove: ar(ΔADE) = ar(ΔBCF).
Proof: ∵ ABCD is a || gm
∴ AB || DC ...(1)
| Opposite sides of a || gm are ||
∵ DCFE is a || gm
∴ DC || EF ...(2)
| Opposite sides of a || gm are ||
From (1) and (2),
AB || EF ...(3)
∵ ABCD is a || gm
∴ AD = BC ...(4)
| Opposite sides of a || gm are equal
∵ ΔADE and ΔBCF are on equal bases (∵ AD = BC) and between the same parallels AB and EF.
□∴ ar(ΔADE) = ar(ΔBCF).
∵ Two triangles on the same base (or equal bases) and between the same parallels are equal in areas
