BE and CF are two equal altitudes of a triangle ABC. Using RHS congrue

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

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

Answer»

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.