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ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal.

3.  ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig.). Show that these altitudes are equal.

                

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Consider \Delta AEB   and  \Delta AFC,

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

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

(iii)    AB\ =\ AC              (Given)

Thus by AAS congruence axiom, we can conclude that :

                                 \Delta AEB\ \cong \Delta AFC

Now, by c.p.c.t. we can say :     BE\ =\ CF

Hence these altitudes are equal.

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