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AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC (ii) AD bisects A. Q.2

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Find the simplest solution of ncert class 9th of chapter triangles . Please help me to solve the best solution of exercise 7.3 question number 2 . How i solve this question in a simplest and easiest way please help me to find out this question. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC (ii) AD bisects A.

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  1. It is given that AD is an altitude and AB = AC. The diagram is as follows:

    Ncert solutions class 9 chapter 7-18

    (i) In ΔABD and ΔACD,

    ADB = ADC = 90°

    AB = AC (It is given in the question)

    AD = AD (Common arm)

    ∴ ΔABD ΔACD by RHS congruence condition.

    Now, by the rule of CPCT,

    BD = CD.

    So, AD bisects BC

    (ii) Again, by the rule of CPCT, BAD = CAD

    Hence, AD bisects A.

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