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Chapter 8 exercise 8.1 question no. …

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Chapter 8 exercise 8.1 question no. 9 please tell me fast.

    • Posted by Diksha Laniya🐥 2 years, 11 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Sanket ... 2 years, 11 months ago

    AD || BC and BD is a transversal. ∴ ∠ADB = ∠CBD [ ∵ Alternate interior angles are equal] ⇒ ∠ADP = ∠CBQ Now, in ∆APD and ∆CQB, we have AD = CB [Opposite sides of a parallelogram ABCD are equal] PD = QB [Given] ∠ADP = ∠CBQ [Proved] ∴ ∆APD ≅ ∆CQB [By SAS congruency] (ii) Since, ∆APD ≅ ∆CQB [Proved] ⇒ AP = CQ [By C.P.C.T.] (iii) Since, AB || CD and BD is a transversal. ∴ ∠ABD = ∠CDB ⇒ ∠ABQ = ∠CDP Now, in ∆AQB and ∆CPD, we have QB = PD [Given] ∠ABQ = ∠CDP [Proved] AB = CD [ Y Opposite sides of a parallelogram ABCD are equal] ∴ ∆AQB = ∆CPD [By SAS congruency] (iv) Since, ∆AQB = ∆CPD [Proved] ⇒ AQ = CP [By C.P.C.T.] (v) In a quadrilateral ∆PCQ, Opposite sides are equal. [Proved] ∴ ∆PCQ is a parallelogram.

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