**Given :** ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on BD.

**To Prove : **

(i) ∆APB ≅ ∆CQD

(ii) AP = CQ

**Proof :** (i) In ∆APB and ∆CQD, we have

∠ABP = ∠CDQ [Alternate angles]

AB = CD [Opposite sides of a parallelogram]

∠APB = ∠CQD [Each = 90°]

∴ ∆APB ≅ ∆CQD [ASA congruence]

(ii) So, AP = CQ [CPCT] Proved.