question_answer

In \[\Delta ABC\] and \[\Delta DEF\], \[\angle B=\angle E\], \[\angle F=\angle C\] and AB = 3DE. Then, the two triangles are

A) congruent but not similar 

B) similar but not congruent

C) neither congruent nor similar

D) congruent as well as similar

Correct Answer: B

Solution :

In \[\Delta ABC\] and \[\Delta FED\],         \[\angle B=\angle E,\,\angle F=\angle C\] and \[AB=3DE\]

We know that, if in two triangles corresponding two angles are same, then they are similar by AAA similarity criterion. Also,   \[\Delta ABC\]  and \[\Delta DEF\] do not satisfy any rule of congruency, (SAS, ASA, SSS), so both are not congruent.