Q. 64.3( 21 Votes )
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
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
In parallelogram ABCD; Δ APB ≅ Δ CQD
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