In triangles $ABC$ and $DEF$, $\angle B = \angle E$, $\angle F = \angle C$ and $AB = 3\,DE$. Then, the two tr…

Question

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

Accepted Answer

## Model Answer **Option D: Similar but not congruent.** Since ∠B = ∠E and ∠F = ∠C, by AA similarity criterion, △ABC ~ △DEF. But AB = 3DE means corresponding sides are **not** equal, so the triangles are not congruent. ## Explanation - Two equal angles (AA) are sufficient to prove similarity. - Congruence requires equal corresponding sides; since AB = 3DE (ratio 3:1, not 1:1), the triangles differ in size, ruling out congruence. - Examiners expect you to name the criterion (AA) and justify why congruence fails.

Mathematics — CBSE Class 10 board question