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
(a) ∠B = ∠E
(b) ∠A = ∠D
(c)∠B = ∠D
(d) ∠A = ∠F
Solution:
(c) Given, in $\triangle \mathrm{ABC}$ and $\triangle \mathrm{EDF}$,
$\frac{A B}{D E}=\frac{B C}{F D}$
By converse of basic proportionality theorem,
$\triangle A B C \sim \triangle E D F$
Then, $\angle B=\angle D, \angle A=\angle E$
and $\angle C=\angle F$
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