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