Given X and Y are points on the side LN such that;
LX = XY = YN and XZ || LM
To prove: ar (Δ LZY) = (MZYX)
Proof:
Δ XMZ and Δ XLZ are on the same base XZ and between the same parallel lines LM and XZ.
Then, ar (Δ XMZ) = ar (Δ XLZ) ...(i)
On adding ar (Δ XYZ) both sides of eq (i), we get,
ar (ΔXMZ) + ar (ΔXYZ) = ar (Δ XLZ) + ar (Δ XYZ)
⇒ ar (MZYX) = ar (Δ LZY)