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In ΔABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ΔABC is an isosceles triangle in which AB = AC. Q.2

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What is  the ncert class 9th question of chapter triangles of exercise 7.1 question number 2. Please give me the simplest and easiest solution of this question , also give me the best solution of this question. its very important question of this chapter please solve this in a easy way.In ΔABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ΔABC is an isosceles triangle in which AB = AC.

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  1. Solution:

    It is given that AD is the perpendicular bisector of BC

    To prove:

    AB = AC

    Proof:

    In ΔADB and ΔADC,

    AD = AD (It is the Common arm)

    ADB = ADC

    BD = CD (Since AD is the perpendicular bisector)

    So, ΔADB ΔADC by SAS congruency criterion.

    Thus,

    AB = AC (by CPCT)

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