1.

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

Answer»

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



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