# ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that(i) Δ APB ≅ Δ CQD(ii) AP = CQ Given:- ABCD is parallelogram

Formula used :- AAS property

If 2 angles and any one side is are equal in both triangle

Then both triangles are congruent

Solution:-

In Δ APB and Δ CQD

CQD= APB=90°

If ABCD is a parallelogram

CDB= DBA [alternate angles as DC||AB]

AB=DC [opposite sides of parallelogram are equal]

By AAS property

Δ APB Δ CQD

If Δ APB Δ CQD

Then

AP=CQ

Conclusion:-

In parallelogram ABCD; Δ APB Δ CQD

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