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.