ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that
(i) ΔAPB≅ΔCQD
(ii) AP=CQ
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Given:- ABCD is a parallelogram
AP and CQ are perpendiculars, therefore, CQD = BPA = 90°
proof:- in ∆APB and ∆CQD,
CQD = BPA. ( each 90° )
DBA = BDC. ( alternate angles )
DC = AB. ( opposite sides of a parallelogram are equal )
Therefore, by AAS criteria ∆ABP is congurent ∆BPA
Now by cpct AP = CQ
AP and CQ are perpendiculars, therefore, CQD = BPA = 90°
proof:- in ∆APB and ∆CQD,
CQD = BPA. ( each 90° )
DBA = BDC. ( alternate angles )
DC = AB. ( opposite sides of a parallelogram are equal )
Therefore, by AAS criteria ∆ABP is congurent ∆BPA
Now by cpct AP = CQ
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