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13/07/2021 11:56 am
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ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Figure). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ
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13/07/2021 11:58 am
(i) In ΔAPB and ΔCQD,
∠ABP = ∠CDQ (Alternate interior angles)
∠APB = ∠CQD (= 90o as AP and CQ are perpendiculars)
AB = CD (ABCD is a parallelogram)
ΔAPB ≅ ΔCQD [AAS congruency]
(ii) As ΔAPB ≅ ΔCQD.
AP = CQ [CPCT]