Question
Angles A, B, C of a triangle ABC are equal to each other. Prove that $\triangle\text{ABC}$ is equilateral.
✓
Answer
Given that angles A, B, C of a triangle ABC equal to each other.
We have to prove that $\triangle\text{ABC}$ is equilateral
We have, $\angle\text{A}=\angle\text{B}=\angle\text{C}$
Now,
$\angle\text{A}=\angle\text{B}$
BC = AC [opposite sides to equal angles are equal]
And $\angle\text{B}=\angle\text{C}$
$\text{AC}=\text{AB}$
From the above we get
$\text{AB}=\text{BC}=\text{AC}$
$\triangle\text{ABC}$ is equilateral.
We have to prove that $\triangle\text{ABC}$ is equilateral
We have, $\angle\text{A}=\angle\text{B}=\angle\text{C}$
Now,
$\angle\text{A}=\angle\text{B}$
BC = AC [opposite sides to equal angles are equal]
And $\angle\text{B}=\angle\text{C}$
$\text{AC}=\text{AB}$
From the above we get
$\text{AB}=\text{BC}=\text{AC}$
$\triangle\text{ABC}$ is equilateral.
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