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Question
Show that every equiangular triangle is equilateral.
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Solution
△ABC is an equiangular
∠A=∠B=∠C
In △ABC
∠B=∠C
AC=AB ( sides of opposite to equal angles )
Similarly, ∠C=∠A
BC=AB
From (i) and (ii)
Ab=BC=AC
△ABC is an equilateral triangle
∠A=∠B=∠C
In △ABC
∠B=∠C
AC=AB ( sides of opposite to equal angles )
Similarly, ∠C=∠A
BC=AB
From (i) and (ii)
Ab=BC=AC
△ABC is an equilateral triangle
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