question_answer

If in triangles ABC and DEF, \[\frac{AB}{DE}=\frac{BC}{FD},\] then they will be similar, when: (NCERT EXEMPLAR)

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

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

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

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

Correct Answer: C

Solution :

[c] Given, in \[\Delta ABC\] and \[\Delta EDF,\]\[\frac{AB}{DE}=\frac{BC}{FD}\]

So.     \[\Delta ABC\tilde{\ }\Delta EDF\]

if      \[\angle B=\angle D\]    (By ASS similarity criterion)