Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

Answer 1

In ∆AEB and ∆AFC, 

∠AEB and ∠AFC (Each 90º) A 

=∠A (Common angle)

AB = AC (Given)

∠∆AEB  ∠∆AFC (By AAS congruence rule) 

∴ BE = CF (By CPCT)