ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32) Show that:

(i) Δ ABE Δ ACF


(ii) AB = AC, i.e., ABC is an isosceles triangle



It is given in the question that:

BE = CF


(i) In


A = A (Common)


AEB = AFC (Right angles)


BE = CF (Given)


Therefore,


By AAS axiom,



(ii) Thus,


AB = AC (By c.p.c.t)


Therefore,


ABC is an isosceles triangle


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