Question

In the given figure, BE and CF are two equal altitudes of ΔABC.
Show that (i) ΔABE ≅ ΔACF, (ii) AB = AC.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{ABE}\mathrm{and}△\mathrm{ACF},\mathrm{we}\mathrm{have}: \\ \mathrm{BE}=\mathrm{CF}\left(\mathrm{Given}\right) \\ \angle \mathrm{BEA}=\angle \mathrm{CFA}=90° \\ \angle \mathrm{A}=\angle \mathrm{A}\left(\mathrm{Common}\right) \\ △\mathrm{ABE}\cong △\mathrm{ACF}(\mathrm{AAS}\mathrm{criterion}) \end{gathered}$$
AB = AC (CPCT)