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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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In triangles POA  and BOR
∠ 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)
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