Answer :

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Δ ABC is an equiangular triangle


Let AD be the perpendicular from A on BC


In Δ ABD and Δ ACD


ABD = ACD (ΔABC is equiangular)


ADB = ADC (AD is a perpendicular)


AD = AD (Common side)


So Δ ABD and Δ ACD are congruent to each other by A.A.S. axiom of congruency


AB = AC (Corresponding Parts of Congruent Triangles)


BD = DC(Corresponding Parts of Congruent Triangles)


Since the triangle is equiangular and AB = AC , so


AB = AC = BC


Hence the triangle is equilateral


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