# PQRS is a parallelogram whose diagonals meet at O. a line through O intersects PQ at A and RS at B. Show that ar(△AOP) = ar(△BOR)

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∠ POA = ∠BOR (Vertically opp angles)

∠BRO = ∠OPA ( alternate interior angles )

OP = OR (diagonals bisect each other)

By ASA congruence property

ΔPOA is congruence to ΔBOR

Therefore, ar(ΔPOR) = ar(ΔBOR)