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ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig. 7.17). Prove that (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC. Q.2

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Sir please help me to solve the ncert class 9th solution of chapter triangles.How I solve this question of exercise 7.1 question number 2. Find the simplest and easiest solution of this question , also give me the best solution of this question .ABCD is a quadrilateral in which AD = BC and DAB = CBA (see Fig. 7.17). Prove that (i) ΔABD ΔBAC (ii) BD = AC (iii) ABD = BAC.

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  1. The given parameters from the questions are DAB = CBA and AD = BC.

    (i) ΔABD and ΔBAC are similar by SAS congruency as

    AB = BA (It is the common arm)

    DAB = CBA and AD = BC (These are given in the question)

    So, triangles ABD and BAC are similar i.e. ΔABD ΔBAC. (Hence proved).

    (ii) It is now known that ΔABD ΔBAC so,

    BD = AC (by the rule of CPCT).

    (iii) Since ΔABD ΔBAC so,

    Angles ABD = BAC (by the rule of CPCT).

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