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

Solution

Given

Given: 

Altitude BE and CF are equal

To prove:

 ΔABC is an isosceles Δ

In ΔBEC and ΔCEB

∠E=∠F —————-[each 90°] 

BC=BC —————–[common]

BF=CF —————-[given]

 ΔBEC ≅ ΔCEB [R.H.S]

∠C=∠B ————-[C.P.C.T]

 In ΔABC,

∠C=∠B

Therefore, AB = AC as sides opposite to the equal angles is always equal.

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