ABCD is a parallelogram in which perpendiculars BP and DQ are drawn on the diagonal AC from the points B and D respectively.Prove that BPDQ is a parallelograml
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It is given that in parallelogram ABCD, BP is perpendicular to AC and DQ is perpendicular to AC.
In ΔADQ and ΔCBP,
AD=CD (Opposite sides of a parallelogram)
∠DAQ=∠BCP and AD∣∣BC,AC (Transversal alternate angles)
∠DQA=∠BPC=90
0
(Given)
⸫ΔADQ=ΔCBP (SAA)
⸫BP=DQ (C.P.C.T)
Hence proved.
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