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here, in the figure,
in ΔABD & ΔACD,
AD = AD ( common )
∠ADB = ∠ADC ( AD⊥ BC )
∠BAD = ∠CAD ( AD is the bisector of ∠A )
∴ ΔABD ≅ ΔACD ( ASA congruency )
By CPCT, AB = AC
∴ ΔABC is an isosceles triangle
Hope it helps...
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