Question : If in $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}, \frac{A B}{D E}=\frac{B C}{F D}$, then they will be similar when:
Option 1: $\angle B=\angle D$
Option 2: $\angle A=\angle D$
Option 3: $\angle A=\angle F$
Option 4: $\angle B=\angle E$
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Correct Answer: $\angle B=\angle D$
Solution :
$\frac{AB}{DE} = \frac{BC}{FD}$
⇒ $\frac{AB}{BC} = \frac{DE}{FD}$
Angle between $AB$ and $BC$ is $\angle B$ and angle between $DE$ and $FD$ is $\angle D$.
$\therefore$ They will be similar when these angles will be equal, i.e, $\angle B = \angle D$
Hence, the correct answer is $\angle B = \angle D$.
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