Question

In the given figure, BE ⊥ CA and CF ⊥ BA such that BE = CF. Then, which of the following is true?
(a) ∆ABE ≅ ∆ACF
(b) ∆ABE ≅ ∆AFC
(c) ∆ABE ≅ ∆CAF
(d) ∆ABE ≅ ∆FAC

Answer 1

(a) $△ABE\cong △ACF$

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