The Total solution for NCERT class 6-12
ABCD is aparallelogram and AP and CQ are perpendiculars from vertices A and C ondiagonal BD (see Fig. 8.21). Show that
(i) ΔAPB ≅ ΔCQD
(ii) AP = CQ
(i) In ΔAPB and ΔCQD,
∠ABP = ∠CDQ (Alternate interior angles)
∠APB = ∠CQD (= 90o asAP and CQ are perpendiculars)
AB = CD (ABCD is a parallelogram)
, ΔAPB ≅ ΔCQD[AAS congruency]
(ii) As ΔAPB ≅ ΔCQD.