Answer :

Given, ABCD is a parallelogram.

BC = AD and BC||AD

Also, DC = AB and DC||AB

Since, P is mid-point of DC.

DP = PC = DC

Now, QC||AP and PC||AQ

APCQ is a parallelogram.

AQ = PC = DC = AB = BQ

Now, in ΔAQR and ΔBQC,

BQ = AQ

∠BQC = ∠AQR

And ∠BCQ = ∠ARQ

ΔAQR BQC

AR = BC

But BC = DA

AR = DA

Also, CQ = QR

Hence, Proved.

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