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Question

ABCD is a parallelogram and AP andCQ are perpendiculars from vertices A and C on diagonal BD.

Show that (i)ΔAPBΔCQD

(ii)AP=CQ


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Solution

Step 1: Drawing the diagram:

ABCD is a parallelogram

AP and CQ are perpendiculars from vertices A and C on diagonal BD.

Step 2: Proving ΔAPBΔCQD:

In, ΔAPB and ΔCQD

APB=CQD(Eachequalsto90°)ABP=CDQ(AlternateinterioranglesforABCD)AB=CD(OppositesidesofparallelogramABCDareequal)

APBCQD(ByAAScongruencycriteria)

Step 3: Proving AP=CQ

AP=CQ(ByCPCT)

Hence proved.


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