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Question

Question 4
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.


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Solution


In ΔBEC and ΔCFB
BEC=CFB (each 90)
BC = CB (common)
BE = CF (given)
ΔBECΔCFB (by RHS congruency)
BCE=CBF (by CPCT)
AB = AC (Sides opposite to equal angles of a triangle are equal)
Hence, ΔABC is isosceles.


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