Question

. Prove that AABC is an equilateral triangle if the altitudes of AABC are equal. equilateral triangle are equal​

Answer 1

Answer:

In right-angle triangles BCE and CBF, we have,

BC = BC   (common hypotenuse);

BE = CF   (given).

Hence BCF and CBF are congruent, by RHS theorem. Comparing the triangles, we get ∠B=∠C.

This implies that

AC = AB   (sides opposite to equal angles).

Similarly,

AD=BE⇒∠B=∠A

⇒AC=BC

Together, we get AB=BC=ACor △ABC is equilateral. [henceproved]

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