Given that:
AD=AE,BD=ECTo prove: AB=AC
Since, AD=AE △ADE is an isosceles triangle.
AF⊥DE,DF=FE (Properties of isosceles triangle)
Now, BD+DF=FE+EC⇒BF=FC
In △AFB and △AFC,
⇒BF=FC
∠AFB=∠AFC
⇒AF is common side
Thus △AFB≅AFC
Therefore, AB=AC .....(By CPCT)
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