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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

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Question

Show that every equiangular triangle is equilateral.

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Solution

$△ A B C$ is an equiangular
$∠ A = ∠ B = ∠ C$
In $△ A B C$
$∠ B = ∠ C$
$A C = A B$ ( sides of opposite to equal angles )
Similarly, $∠ C = ∠ A$
$B C = A B$
From (i) and (ii)
$A b = B C = A C$
$△ A B C$ is an equilateral triangle

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"If Two Sides of a Triangle are Unequal, Then the Angle Opposite to the Greater Side is Greater

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If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Standard IX Mathematics

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Show that every equiangular triangle is equilateral.

△ABC is an equiangular∠A=∠B=∠CIn △ABC∠B=∠CAC=AB ( sides of opposite to equal angles )Similarly, ∠C=∠ABC=ABFrom (i) and (ii)Ab=BC=AC△ABC is an equilateral triangle

$△ A B C$ is an equiangular
$∠ A = ∠ B = ∠ C$
In $△ A B C$
$∠ B = ∠ C$
$A C = A B$ ( sides of opposite to equal angles )
Similarly, $∠ C = ∠ A$
$B C = A B$
From (i) and (ii)
$A b = B C = A C$
$△ A B C$ is an equilateral triangle