ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ

To prove : (i) ΔAPB ≅ ΔCQD \(since AB parallel DC\) and transversal BD. \(angle ABP=angle CDQ\) ————- (1) \(bigtriangleup APB=bigtriangleup CQD\) \(angle ABP = angle CDQ\) AB=CD \(bigtriangleup APB cong bigtriangleup CQD\) Therefore, AP = CQ.

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