7. In triangles \(ABC\) and \(DEF\), if \(\angle B=\angle E\), \(\angle F=\angle C\) and \(AB=3\,DE\), the triangles are
congruent but not similar
similar but not congruent
neither
congruent as well as similar
Step 1: We are told that \(\angle B = \angle E\) and \(\angle F = \angle C\).
This means two angles of triangle \(ABC\) are equal to two angles of triangle \(DEF\).
Step 2: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar by the AA (Angle–Angle) similarity rule.
Step 3: To be congruent, all sides of the two triangles must be exactly the same length (or have the same ratio of 1:1).
But here, \(AB = 3 \times DE\). So the ratio of sides is \(3:1\), not \(1:1\).
Step 4: Therefore, the triangles are similar (because of equal angles), but not congruent (because the sides are not equal in length).
Final Answer: Similar but not congruent.