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Here, ABCD is a parallelogram.
AB∥DC and BD is a transversal.
Angle ABP = Angle CDQ (Alternate angles) - - 1
In triangle APB and triangle CQD
AB = CD.....(opposite sides of parallelogram are equal )
angle ABP = angle CDQ ( From 1 )
BP = DQ ( Given )
Triangle ABP is congruent to tri CQD ( By SAS congruence)
AP = CQ ( CPCT)
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