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In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that: (i) ΔAPD ≅ ΔCQB (ii) AP = CQ Q.9(1-2)

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How i solve the question of class 9th ncert math of Quadrilaterals chapter of exercise 8.1of question no 9. I think it is very important question of class 9th give me the tricky way for solving this question In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that: (i) ΔAPD ≅ ΔCQB (ii) AP = CQ

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  1. (i) In ΔAPD and ΔCQB,

    DP = BQ (Given)

    ∠ADP = ∠CBQ (Alternate interior angles)

    AD = BC (Opposite sides of a parallelogram)

    Thus, ΔAPD ≅ ΔCQB [SAS congruency]

    (ii) AP = CQ by CPCT as ΔAPD ≅ ΔCQB.

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