In $\Delta ABC$ and $\Delta DEF$, $\angle B = \angle E, \angle F = \angle C$ and $AB = 3 DE$. Then the two triangles are:
Congruent but not similar
Similar but not congruent
Neither congruent nor similar
Congruent as well as similar
Step-by-Step Solution
Key Concept: Two angles equal $\Rightarrow \text{AA similarity}$. Side lengths $AB = 3 DE <br>eq DE \Rightarrow \text{not congruent}$.
Stepwise Solution:
Since two pairs of corresponding angles are equal ($\angle B = \angle E, \angle C = \angle F$), by AA criterion, $\Delta ABC \sim \Delta DEF$. [0.5 Mark]
Since $AB = 3 DE$, the ratio of sides is $3:1
eq 1$, so they are not congruent. Hence, similar but not congruent. [0.5 Mark]
Marking Scheme:
• AA similarity test: 0.5 Mark
• Non-congruence test ($AB
eq DE$): 0.5 Mark
Correct Answer: Similar but not congruent