Question

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Answer 1

Data : BE and CF are two equal altitudes of a triangle ABC. 

To Prove: 

ABC is an isosceles triangle. 

Proof : BE = CF (data) 

In ∆BCF and ∆CBE, 

∠BFC = ∠CEB = 90° 

(data) BC is common hypotenuse. 

As per Right angle, 

hypotenuse, side postulate, 

∴ ∆BCF ≅ ∆CBE 

∴ ∠CBF = ∠BCE 

∴ ∠CBA = ∠BCA 

∴ AB = AC 

∴ ∆ABC is an isosceles triangle.