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

In ∆BEC and ∆CFB, 

∠BEC = ∠CFB (Each 90°) 

BC = CB (Common) 

BE = CF (Given) 

∠∆BEC ≅ ∠∆CFB (By RHS congruency) 

∠BCE = ∠CBF (By CPCT) 

∠AB = AC (Sides opposite to equal angles of a triangle are equal) 

Hence, ∆ABC is isosceles.