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

**Solution:**

Let's construct a diagram according to the given question as shown below.

In ΔBEC and ΔCFB,

∠BEC = ∠CFB (Each 90°)

BC = CB (Common)

BE = CF (altitudes are equal given)

∴ ΔBEC ≅ ΔCFB (By RHS congruency)

∴ ∠BCE = ∠CBF (By CPCT)

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

Hence, ΔABC is isosceles.

**Video Solution:**

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

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.3 Question 4:

**Summary:**

If BE and CF are two equal altitudes of a triangle ABC, then using the RHS congruence rule, we can prove that the triangle ABC is isosceles.