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ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that (i) ∆ABE ≅ ∆ ACF

4.(i) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that

(i) \small \Delta ABE \cong \Delta ACF

             

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Consider \Delta ABE  and  \Delta ACF ,

(i)    \angle A  is common in both the triangles.

(ii)    \angle AEB\ =\ \angle AFC              (Right angles)

(iii)   BE\ =\ CF                             (Given)

Thus by  AAS congruence, we can say that :

                                              \small \Delta ABE \cong \Delta ACF   

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