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In parallelogram ABCD, two points P and...

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that `D P = B Q`. Show that:
(i) `DeltaA P D~= DeltaC Q B`
(ii) `A P = C Q`
(iii) `DeltaA B C`
(iv) `A Q = C P`
(v) APCQ is a parallelogram.

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