Question

In triangle ABC, altitudes BE and CF are equal. Prove that the triangle is isosceles.

Answer 1

In ΔABE and ΔACF,
∠A = ∠A .........[Common]
∠AEB = ∠AFC = 90° ......[Given: BE ⊥ AC; CF ⊥ AB]
BE = CF ..........[Given]

∴ ΔABE ≅ ΔACE .........[AAS Criterion]
⇒ AB = AC
Therefore, ABC is an isosceles triangle.