# ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at

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ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at R, show that: (i) APCQ is a parallelogram.(ii) DPBQ is a parallelogram.(iii) PSQR is a parallelogram

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ABCD is a parallelogram
PQ=CQ=1/2DC
AP=PB=1/2AB
:.AP=CQ=1/2AB
AB||CD
:.AB||CQ
SQ||PR(AQCP)
PS||QR(DPBQ)