In `DeltaABC and DeltaDEF`, `angleB=angleE,angleF=angleC` and AB=3DE. Then, the two triangles are

Options

A. congruent but not similar
B. similar but not congruent
C. neither congruent nor similar
D. congruent as well as similar

Explanation

To solve the problem, we need to analyze the given information about triangles \( \Delta ABC \) and \( \Delta DEF \).

### Step-by-Step Solution:

1. **Identify Given Information**:
- \( \angle B = \angle E \)
- \( \angle F = \angle C \)
- \( AB = 3 \times DE \)

2. **Use Angle-Angle (AA) Similarity Criterion**:
- Since two angles of triangle \( \Delta ABC \) are equal to two angles of triangle \( \Delta DEF \), we can conclude that the triangles are similar by the AA similarity criterion.
- Therefore, we can write:
\[ \Delta ABC \sim \Delta DEF \]

3. **Determine the Relationship of Sides**:
- From the similarity of triangles, we know that the ratios of the corresponding sides are equal. Thus, we can express this as:
\[ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \]
- Given \( AB = 3 \times DE \), we can substitute this into our ratio:
\[ \frac{3 \times DE}{DE} = 3 \]
- This implies that the side \( AB \) is three times the side \( DE \).

4. **Conclusion about Congruence**:
- For two triangles to be congruent, all corresponding sides must be equal. Here, we have established that \( AB \) is not equal to \( DE \) (since \( AB = 3 \times DE \)).
- Therefore, while the triangles are similar, they are not congruent.

5. **Final Statement**:
- We conclude that \( \Delta ABC \) is similar to \( \Delta DEF \) but not congruent.

### Final Answer:
The two triangles are similar but not congruent.

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