Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
In \(\triangle{ABE}\) and \(\triangle{ACF}\) , we have,
\(\angle{AEB}\) = \(\angle{AFC}\)(\(\because BE and CF are perpendicular to sides AC and AB)
\(\angle{BAE}\) = \(\angle{CAF}\) ...(\(\because \(\angle{A}\) is the Common angle)
and BE = CF ...(Given)
\(\therefore \) \(\triangle{ABE}\) \(\displaystyle \cong \) \(\triangle{ACF}\) ...(By AAS Congruency test)
Thus, AB = AC ...(By CPCT)
\(\therefore \) \(\triangle{ABC}\) is an isosceles triangle.
Hence, proved.