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Question
In ΔABC, AD is the perpendicular bisector of BC (see the given figure). Show that ΔABC is an isosceles triangle in which AB = AC.
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Solution
Since AD is the bisector of BC.
∴ BD = CD
Now, in △ABD and △ACD, we have
AD = DA ...[Common]
∠ADB = ∠ADC ...[Each 90°]
BD = CD ...[Proved above]
∴ △ABD ≌ △ACD ...[By SAS congruence]
⇒ AB = AC ...[By Corresponding parts of congruent triangles]
Thus, △ABC is an isosceles triangle.
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