ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that
ar(Δ POA) = ar(Δ QOC)
In ΔPOA and QOC, we have
∠AOP = ∠COQ (Vertically opposite angle)
OA = OC (Diagonals of parallelogram bisect each other)
∠PAC = ∠QCA (AB ‖ DC, alternate angles)
So, by ASA congruence rule, we have
ΔPOA ≅ ΔQOC
Area (ΔPOA) = Area (ΔQOC)
Hence, proved