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.

☛ Check: NCERT Solutions for Class 9 Maths Chapter 7

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.

☛ Related Questions:

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