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ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersect AB at P and DC at Q. Prove that:

ar(POA) = ar(QOC)

Asked by Topperlearning User 10th December 2013, 10:02 AM
Answered by Expert
Answer:

In POA and QOC, we have

AOP = COQ [vertical opp. angle]

AO = OC [diagonals of a ||gm bisect each other]

PAC = QCA [ alt. interior angles]

[ASA criteria]

[congruent figures are equal in areas]

Answered by Expert 10th December 2013, 12:02 PM
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