Q. 184.8( 10 Votes )

P is the mid-poin

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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