Question : If in $\triangle PQR$ and $\triangle DEF, \angle P=52^{\circ}, \angle Q=74^{\circ}, \angle R=54^{\circ}, \angle D=54^{\circ}, \angle E=74^{\circ}$ and $\angle F=52^{\circ}$, then which of the following is correct?
Option 1: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$
Option 2: $\triangle \mathrm{RQP} \sim \triangle \mathrm{FED}$
Option 3: $\triangle \mathrm{PRQ} \sim \Delta \mathrm{FED}$
Option 4: $\triangle \mathrm{PQR} \sim \triangle \mathrm{DEF}$
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Correct Answer: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$
Solution :
$\because$ $\angle P=\angle F=52^0$
$\angle Q=\angle E=74^0$
And $\angle R=\angle D=54^0$
By AAA criteria, triangles are similar.
So, $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$.
Hence, the correct answer is $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$.
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