Question

Question 10
If in $\Delta ABCand\Delta EDF,\frac{AB}{DE}=\frac{BC}{FD}$, then they will be similar, when

(A) $\angle B=\angle E$
(B) $\angle A=\angle D$
(C) $\angle B=\angle D$
(D) $\angle A=\angle F$

Answer 1

(C) $\angle B=\angle D$

Given, in $\Delta ABCand\Delta EDF$
$\frac{AB}{DE}=\frac{BC}{FD}$



By converse of basic proportionality theorem,
$\Delta ABC\sim \Delta EDF$,
Then, $\angle B=\angle D,\angle A=\angle E$
And $\angle C=\angle F$