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Answer :
In \(\triangle{ABE}\) and \(\triangle{ACF}\) , we have,
\(\angle{AEB}\) = \(\angle{AFC}\) ...(BE and CF are perpendiculars drawn to sides AC and AB respectively)
Also, \(\angle{A}\) is common angle.
and AB = AC ...(Given)
Therefore, \(\triangle{ABE}\) \(\displaystyle \cong \) \(\triangle{ACF}\) ...(By AAS congruency test)
Therefore, AB = AC ...(By CPCT)
Hence, BE = CF ...(By CPCT)
Hence, proved.