## ABCD is a parallelogram in which P and Q are midpoints of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show

Question

ABCD is a parallelogram in which P and Q are midpoints of opposite sides AB and CD. 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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2021-08-14T15:08:00+00:00
2021-08-14T15:08:00+00:00 2 Answers
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## Answers ( )

Answer:I think it helps you ⬇⬇Step-by-step explanation:(1)AB║CD and AB=DC⇒AP║QC and 1/2AB=1/2DC⇒AP║QC and AP=QC∴APCQ is a parallelogram(2)AB║DC and AB=DC⇒PB║DQ and 1/2AB=1/2DC⇒PB║DQ and PB=DQ∴DPBQ is a parallelogram(3)PC║AQ [∵APCQ is a parallelogram]∴SO║PRand DP║QB [∵DPBQ is a parallelogram]∴PS║QR∴PSQR is a parallelogram∴Hence provedAnswer:(i) APCQ is a parallelogram. (ii) DPBQ is a parallelogram (iii) PSQR is a parallelogram

Step-by-step explanation:Given: ABCD is a parallelogram

PQ=CQ=1/2DC

AP=PB=1/2AB

∴AP=CQ=1/2AB

AB||CD

∴AB||CQ (AQCP) Therefore, (i) APCQ is a parallelogram.

simillarly,

DP||BQ (DPBQ) Therefore, (ii) DPBQ is a parallelogram.

PS||QR (PSQR) Therefore, (iii)PSQR is a parallelogram