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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