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

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Find this important question of ncert class 9th of chapter triangles .Sir please help me to find out the easiest and simplest solution of question 4 of exercise 7.3, give me the best solution of this question. 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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  1. Ncert solutions class 9 chapter 7-20.

    Solution:

    It is known that BE and CF are two equal altitudes.

    Now, in ΔBEC and ΔCFB,

    BEC = CFB = 90° (Same Altitudes)

    BC = CB (Common side)

    BE = CF (Common side)

    So, ΔBEC ΔCFB by RHS congruence criterion.

    Also, C = B (by CPCT)

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

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