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Question

In ABC,AD is the perpendicular bisector of BC. Show that ABC is an isosceles triangle in which AB=AC.
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Solution

In ABD and ACD, we have

DB=DC Given

ADB=ADC since ADBC

AD=AD Common

by SAS criterion of congruence, we have.

ABDACD

AB=AC Since corresponding parts of congruent triangles are equal

Hence, ABC is isosceles.

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