Question : For congruent triangles $\triangle$ABC and $\triangle$DEF, which of the following statements is correct?
Option 1: Perimeter of $\triangle \mathrm{ABC}=\frac{1}{2}$ Perimeter of $\triangle \mathrm{DEF}$
Option 2: Perimeter of $\triangle \mathrm{ABC}=$ Perimeter of $\triangle \mathrm{DEF}$
Option 3: Perimeter of $\triangle \mathrm{ABC}<$ Perimeter of $\triangle \mathrm{DEF}$
Option 4: Perimeter of $\triangle \mathrm{ABC}>$ Perimeter of $\triangle \mathrm{DEF}$
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Correct Answer: Perimeter of $\triangle \mathrm{ABC}=$ Perimeter of $\triangle \mathrm{DEF}$
Solution :
For congruent triangles $\triangle {ABC}$ and $\triangle {DEF}$,
$AB = DE$, $BC = EF$, $AC=DF$
So, $AB+BC+AC=DE+EF+DF$
So, perimeter of $\triangle \mathrm{ABC}=$ Perimeter of $\triangle \mathrm{DEF}$
Hence, the correct answer is 'Perimeter of $\triangle \mathrm{ABC}=$ Perimeter of $\triangle \mathrm{DEF}$.
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