Q

# 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) $\small \Delta ABE \cong \Delta ACF$

Views

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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