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)
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]
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