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.