Suppose ABC is an equiangular triangle . Prove that it is equilateral . ( You have seen earlier that an equilateral triangle is equiangular . is equivalent id equilaterality .

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Solution

ABC is an equiangular triangle i.e,
$∠ A = ∠ B = ∠ C$
$∠ A = ∠ B$
$B C = A C . . . . (i)$ [Theorem 2 ]
$∠ A = ∠ C$
$∴ B C = A B . . . (i)$ [ Theorem 2]
From (i) and (ii)
$A B = B C = A C$
$∴△ A B C$ is equilateral

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Suppose ABC is an equiangular triangle . Prove that it is equilateral . ( You have seen earlier that an equilateral triangle is equiangular . is equivalent id equilaterality .

ABC is an equiangular triangle i.e,∠A=∠B=∠C∠A=∠BBC=AC....(i) [Theorem 2 ]∠A=∠C∴BC=AB...(i) [ Theorem 2] From (i) and (ii) AB=BC=AC∴△ABC is equilateral

ABC is an equiangular triangle i.e,
$∠ A = ∠ B = ∠ C$
$∠ A = ∠ B$
$B C = A C . . . . (i)$ [Theorem 2 ]
$∠ A = ∠ C$
$∴ B C = A B . . . (i)$ [ Theorem 2]
From (i) and (ii)
$A B = B C = A C$
$∴△ A B C$ is equilateral