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In Δ APB and Δ CQD
AB = CQ (∵opposite sides of a parallelogram are equal)
∠APB = ∠CDQ = 90°
∠ABP = ∠ CQD (∵ interior alternate angles)
∴ By AAS congruency, Δ APB ≅ Δ CQD
Hence Proved
AP = CQ (∵ corresponding parts of congruent triangles are equal)
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