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Given ABCD is a parallelogram.
As opposite angles are equal in a parallelogram;
∠A = ∠C
Again given, AP and CQ are bisector of angle A and C, respectively.
1/2∠A = 1/2∠C
∠APD = ∠QCD
Hence, AP II CQ.
Then,
Also, in AQCP
As, AB II DC, so AQ II PC.
Also, AP II CQ.
So, AQCP is a parallelogram.
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