Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?
Option 1: DF = 5 cm, $\angle$E = 60°
Option 2: DE = 5 cm, $\angle$F = 60°
Option 3: DE = 5 cm, $\angle$D = 60°
Option 4: DE = 5 cm, $\angle$E = 60°
Correct Answer: DF = 5 cm, $\angle$E = 60°
Solution :
According to the question,
$\triangle$ABC $\cong$ $\triangle$FDE then,
∴ AB = FD, BC = DE and CA = EF
And, $\angle$A = $\angle$F = 80º, $\angle$B = $\angle$D = 40º, $\angle$C = $\angle$E
Through the Sum of angles,
180º = $\angle$A + $\angle$B + $\angle$C
⇒ 180º = 80º + 40º + $\angle$C
⇒ 180º = 120º + $\angle$C
⇒ 180º – 120º = $\angle$C
⇒ $\angle$C = 60º
Since, $\angle$C = $\angle$E then $\angle$E = 60º
Hence, the correct answer is 'DF = 5 cm, $\angle$E = 60º'.
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