question_answer

If in \[\Delta ABC\] and \[\Delta DEF\], \[\frac{AB}{DE}=\frac{BC}{FD}\], then they will be similar, when

A) \[\angle B=\angle E\]

B) \[\angle A=\angle D\]

C) \[\angle B=\angle D\]

D) \[\angle A=\angle F\]

Correct Answer: C

Solution :

Given, in \[\Delta ABC\]

and \[\Delta EDF\],\[\frac{AB}{DE}=\frac{BC}{FD}\]

By converse of basic proportionality theorem,

\[\Delta ABC-\Delta EDF\]

Then, \[\angle B=\angle D,\angle A=\angle E\]and \[\angle C=\angle F\]

\[\therefore \,\,\,\,\,\angle B=\angle D\]